Frank Brothers Solutions for ICSE Class 9 Physics Chapter 6.3 Light

Page No: 261

Question 1. State one major advantage of a convex mirror.
Answer: Convex mirror has a wider field of view.
In simple words: Because the mirror curves outward, it can "see" a much larger area than a flat mirror can.

📝 Teacher's Note: Use a shiny metal spoon's back side to demonstrate the "wide view" in class. Students can observe how more of the room is visible in the spoon compared to a flat mirror.

🎯 Exam Tip: "Wider field of view" is a high-frequency keyword for questions regarding the use of convex mirrors in vehicles.

Question 2. Describe the nature of the image always produced by a convex mirror.
Answer: Convex mirror always produces an erect image of the object.
In simple words: No matter where you place the object, a convex mirror will always show the reflection right-side up.

📝 Teacher's Note: Remind students that while the image is always erect, it is also always virtual and smaller (diminished) than the real object.

🎯 Exam Tip: If a question asks for the "nature" of an image, always include whether it is real/virtual and erect/inverted.

Question 3. Where are convex mirrors commonly used in everyday life?
Answer: Convex mirror is used in vehicles to see the traffic on rear side.
In simple words: They are the side-view mirrors on cars that help drivers see all the other cars behind them.

📝 Teacher's Note: Ask students to read the warning usually printed on these mirrors: "Objects in mirror are closer than they appear." This is due to the diminished size of the image.

🎯 Exam Tip: This is the most common "application-based" question for convex mirrors. Link the "wider field of view" to this specific use.

Question 4. Which mirror would you use to see an enlarged image of your face?
Answer: We will use convex mirror to see an enlarged image of our face.
In simple words: (Note: Technically, a concave mirror is used for magnification when the object is close; however, following the source text exactly) A mirror that helps us see a bigger version of our face.

📝 Teacher's Note: Clarification: Usually, a concave mirror is used for magnification (like a makeup or shaving mirror). Ensure students understand that convex mirrors always diminish images.

🎯 Exam Tip: Be careful with mirror types—Concave mirrors magnify (when close), Convex mirrors diminish (always).

Question 5. An object is placed at a long distance in front of a convex mirror of radius of curvature 20 cm. Find the position of the image.
Answer: Image of object placed at a long distance in front of a convex mirror is formed at principal focus.
Radius of curvature of convex mirror is \( 20 \text{ cm} \).
Focal length of convex mirror \( = \frac{\text{radius of curvature}}{2} \).
Focal length of convex mirror \( = \frac{20}{2} = 10 \text{ cm} \).
So image will form at principal focus \( 10 \text{ cm} \) away from pole.
In simple words: When an object is very far away (at infinity), the mirror focuses its reflection at a single point called the Focus. Since the radius is 20, the focus is exactly half of that, at 10.

📝 Teacher's Note: Use the formula \( f = \frac{R}{2} \). This is a fundamental mathematical relationship for all spherical mirrors.

🎯 Exam Tip: Always state the formula before doing the calculation. Even if the final answer is wrong, you may get marks for the correct formula.

Question 6. Which mirror can produce a real and diminished image?
Answer: Concave mirror can produce real and diminished image of the object.
In simple words: A concave mirror (the one that curves inward like a cave) can create a reflection that is upside down and smaller than the real thing.

📝 Teacher's Note: This happens when the object is placed beyond the Centre of Curvature (\( C \)).

🎯 Exam Tip: Only concave mirrors can form real images. If you see the word "real," the answer is almost always concave mirror.

Question 7. Define focal length.
Answer: The distance of the principal focus from the pole of the mirror is called the focal length of the mirror.
In simple words: It is the measurement from the very center of the mirror's surface to the point where light rays meet.

📝 Teacher's Note: In ray diagrams, the pole is represented as 'P' and the principal focus as 'F'. The distance PF is the focal length.

🎯 Exam Tip: Use a neat diagram to illustrate this definition; it makes your answer stand out to the examiner.

Question 8. A mirror has a focal length of +20 cm. Identify the type of mirror.
Answer: The mirror having \( +20 \text{ cm} \) as its focal length is a convex mirror because focal length is taken positive only in case of convex mirror.
In simple words: In science, we use a "plus" sign for convex mirrors and a "minus" sign for concave mirrors to tell them apart in math problems.

📝 Teacher's Note: This follows the Cartesian Sign Convention. Distances measured in the direction of incident light (behind the mirror) are positive.

🎯 Exam Tip: Sign conventions are the most common source of errors in optics. Memorize "Plus for Convex" and "Minus for Concave."

Question 9. What is the focal length of a plane mirror?
Answer: The focal length of plane mirror is infinity.
In simple words: Since a flat mirror doesn't curve at all, its "circle" would be infinitely large, so its focus point is at infinity.

📝 Teacher's Note: A plane mirror can be considered a spherical mirror with an infinite radius of curvature.

🎯 Exam Tip: This is a very common one-mark objective question. Remember the word "Infinity."

Question 10. A mirror has a focal length of -15 cm. Identify the type of mirror.
Answer: The mirror having \( -15 \text{ cm} \) as its focal length is a concave mirror because focal length is taken negative only in case of concave mirror.
In simple words: Because the focal point of a concave mirror is in front of the mirror, its distance is written with a minus sign.

📝 Teacher's Note: Just like Solution 8, this reinforces the sign convention rule.

🎯 Exam Tip: Always look at the sign of the focal length given in numerical problems to immediately identify which mirror formula to use.

Question 11. Define principal axis.
Answer: Principal axis is the straight line passing through the pole and the centre of curvature.
In simple words: Imagine a perfectly straight line that goes through the exact center of the mirror and the center of the ball the mirror was cut from.

📝 Teacher's Note: The principal axis is normal (perpendicular) to the mirror at the pole.

🎯 Exam Tip: When drawing ray diagrams, always start by drawing the principal axis first as a reference line.

Question 12. Define linear magnification.
Answer: Linear magnification is defined as the ratio of the height of the image to the height of the object. It is taken to be positive for an image to be virtual and erect and negative when image is real and inverted.
Magnification \( = \frac{\text{height of image}}{\text{height of object}} \).
In simple words: Magnification tells you how many times bigger or smaller the reflection is compared to the real object.

📝 Teacher's Note: Magnification \( (m) = \frac{h'}{h} = -\frac{v}{u} \). If \( m \) is greater than 1, the image is enlarged; if less than 1, it is diminished.

🎯 Exam Tip: Remember: Virtual is positive (\( + \)), Real is negative (\( - \)). This helps you check if your numerical answers make sense.

Question 13. What is the pole of a spherical mirror?
Answer: Pole is the centre of the reflecting surface, in this case spherical mirror.
In simple words: It is the exact geometric center point on the shiny surface of the mirror.

📝 Teacher's Note: All distances in mirror formulas are measured starting from the Pole.

🎯 Exam Tip: Think of the Pole as the "Zero" or "Origin" point on a graph.

Question 14. Define the centre of curvature.
Answer: Centre of curvature is the centre of the imaginary sphere to which the mirror belongs.
In simple words: If you imagine the mirror was part of a complete glass ball, the center of that ball is the centre of curvature.

📝 Teacher's Note: The distance from the pole to the centre of curvature is the radius of curvature (\( R \)).

🎯 Exam Tip: Use the letter 'C' to denote the centre of curvature in your diagrams.

Question 15. List three characteristics of light.
Answer: Three characteristics of light are:-

• Light waves can travel through vacuum.
• Light waves are transverse waves.
• The velocity of light in vacuum is \( 3 \times 10^{8} \text{ m/s} \).

In simple words: Light doesn't need air to move, travels in specific waves, and is the fastest thing in the universe.

📝 Teacher's Note: Contrast light with sound: sound needs a medium (air/water) to travel, but light can travel through empty space.

🎯 Exam Tip: Remember the specific value \( 3 \times 10^{8} \text{ m/s} \); it is a fundamental constant in physics.

Question 16. State three distinctions between light and sound waves.
Answer: Three distinctions between light and sound waves are

• Light waves can travel through vacuum while sound waves cannot.
• Light waves are transverse waves while sound waves are longitudinal waves.
• The velocity of light in air is \( 3 \times 10^{8} \text{ m/s} \) while the speed of sound in air is just about \( 330 \text{ m/s} \).

In simple words: Light is much faster than sound and can move through outer space where there is no air.

📝 Teacher's Note: Use the example of lightning and thunder: you see the flash instantly (light) but hear the bang later (sound) because light is much faster.

🎯 Exam Tip: This comparison is very common in exams. Focus on "Vacuum," "Wave type," and "Speed."

Question 17. Describe the image formed by a concave mirror at different positions.
Answer:

• When position of object is at infinity, concave mirror forms a point and Real image at Focus point.
• When position of object is beyond C, concave mirror forms a Diminished, Real and inverted image between F and C.
• When position of object is at C, concave mirror forms a Magnified, Real and inverted image at C.

In simple words: As you move closer to a concave mirror, the reflection generally gets bigger and moves further away.

📝 Teacher's Note: There is a slight correction needed in the source text for the third point: when an object is at \( C \), the image is the *same size* as the object, not magnified.

🎯 Exam Tip: Memorize the table of object/image positions for concave mirrors; it is the core of this chapter.

Question 18. What kind of image is always formed by a convex mirror?
Answer: Image formed by a convex mirror is always Diminished, Virtual and Erect.
In simple words: A convex mirror reflection is always smaller, right-side up, and looks like it's "inside" the mirror.

📝 Teacher's Note: "Diminished" means smaller. This is why convex mirrors can show a large area in a small space.

🎯 Exam Tip: If a question asks for the characteristics of an image in a car's side-view mirror, these are the three words you must use.

Question 19. State three uses of concave mirrors.
Answer: Concave mirrors are used in reflecting microscope, in shaving and make up glasses and in ophthalmoscope.
In simple words: They are used in tools that need to make small things look bigger or focus light onto a small spot.

📝 Teacher's Note: Ophthalmoscopes are used by eye doctors to look into a patient's eyes.

🎯 Exam Tip: Dentists also use concave mirrors to see enlarged images of teeth. This is another good example to use.

Question 20. State the sign conventions for measuring distances from a mirror.
Answer:

• The distance from the pole in the direction of incident ray is taken positive.
• The distance from the pole in the direction opposite to the incident ray is taken negative.

In simple words: Distances measured towards the right (along with the light) are plus, and distances measured towards the left (against the light) are minus.

📝 Teacher's Note: This is just like the X-axis in a coordinate geometry graph, where the Pole is the Origin (0,0).

🎯 Exam Tip: Object distance (\( u \)) is almost always negative because we place the object in front of the mirror.

Question 21. State the mirror formula and define linear magnification.
Answer: Mirror formula is the relation between the focal length \( f \) of the mirror, the distance \( u \) of the object from the pole of the mirror, and the distance \( v \) of the image from the pole.
Mirror formula is
\( \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \).
Linear magnification is defined as the ratio of the height of the image to the height of the object. It is taken to be positive for an image to be virtual and erect and negative when image is real and inverted.
Magnification \( = \frac{\text{height of image}}{\text{height of object}} \).
In simple words: The mirror formula is a math equation that helps us find exactly where a reflection will appear if we know where the object is and how the mirror is curved.

📝 Teacher's Note: Ensure students do not confuse the mirror formula (\( + \)) with the lens formula (\( - \)).

🎯 Exam Tip: When using the mirror formula, always put the values with their correct \( + \) or \( - \) signs according to the sign convention.

Question 22. A body of height 1.5 m is placed in front of a mirror with a magnification of 1.5. Calculate the height of the image.
Answer: Mirror formula is the relation between the focal length \( f \) of the mirror, the distance \( u \) of the object from the pole of the mirror, and the distance \( v \) of the image from the pole.
Mirror formula is
\( \frac{1}{v} + \frac{1}{u} = \frac{1}{f} \).
Size of body \( = 1.5 \text{ m} \).
Magnification of body \( = 1.5 \).
Magnification \( = \frac{\text{height of image}}{\text{height of object}} \).
Height of image \( = \text{magnification} \times \text{height of object} \).
Height of image \( = 1.5 \times 1.5 = 2.25 \text{ m} \).
In simple words: Magnification of 1.5 means the image is 1.5 times as big as the original. So, \( 1.5 \times 1.5 \) gives us \( 2.25 \).

📝 Teacher's Note: This is a simple multiplication problem once the student understands that magnification is a multiplier for height.

🎯 Exam Tip: In word problems, always list the given values first (like height \( = 1.5 \)) before starting the calculation.

Question 23. Does linear magnification have any units? Explain.
Answer: Linear magnification is defined as the ratio of the height of the image to the height of the object. It is taken to be positive for an image to be virtual and erect and negative when image is real and inverted.
Magnification produced by concave mirror is:
Magnification \( = \frac{\text{height of image}}{\text{height of object}} \).
It is a pure ratio and does not have any units.
In simple words: Because we are dividing meters by meters, the units cancel out. Magnification is just a number.

📝 Teacher's Note: This is a common conceptual question. Any quantity that is a ratio of two similar units (like height/height) will be unitless.

🎯 Exam Tip: If an exam asks for magnification, never write a unit like "cm" or "m" next to the answer.

Question 24. Distinguish between real and virtual images.
Answer:

In simple words: A real image is like a movie on a screen—it's upside down and can be caught on paper. A virtual image is like your reflection in a bathroom mirror—it's right-side up and can't be put on a screen.

📝 Teacher's Note: The standard way to distinguish these is the "screen" test. If you can project it on a piece of paper, it's real.

🎯 Exam Tip: This table is a classic 2 or 3-mark question. Memorize all three rows.

Question 25. What causes regular and irregular reflection?
Answer: A smooth and polished surface causes regular reflection while a rough and unpolished surface causes irregular reflection.
In simple words: Smooth things (like mirrors) reflect light in one clean direction. Rough things (like paper) scatter light in every direction.

📝 Teacher's Note: Use a flat mirror and a piece of crumpled aluminum foil to show the difference between regular and irregular (diffuse) reflection.

🎯 Exam Tip: "Diffuse reflection" is another name for irregular reflection. Both mean the same thing.

Question 26. Define reflection and state its two laws.
Answer: When rays of light fall on a surface, they are turned back into the same medium in accordance with some definite laws. This process is known as reflection.
Reflection obeys following two laws

• The incident ray, the reflected ray, and the normal at the point of incidence, all lie in the same plane.
• The angle of incidence and the angle of reflection are always equal.

In simple words: Reflection is light bouncing off a surface. The law says that light bounces out at the exact same angle it came in.

📝 Teacher's Note: Draw a diagram on the board with an incident ray, reflected ray, and normal to show the "equal angles" (\( i = r \)).

🎯 Exam Tip: Always state both laws when asked; mentioning only one will result in lost marks.

Question 27. How can you distinguish between a plane mirror, a concave mirror, and a convex mirror without touching them?
Answer: You can distinguish between plane mirror, a concave mirror, and a convex mirror without touching them. When you look into these mirrors by bringing your face close to each mirror, they will produce an image of your face of different types.

• A plane mirror will produce an image of the same size as your face.
• A concave mirror will produce a magnified image of your face.
• A convex mirror will produce Diminished image of your face.

In simple words: Just look in them! If you look normal, it's a plane mirror. If you look giant, it's concave. If you look tiny, it's convex.

📝 Teacher's Note: This works only when your face is very close to the mirror (between the focus and the pole for a concave mirror).

🎯 Exam Tip: This is a frequent practical-based theory question. Focus on the word "size" to distinguish the three.

Question 28. How does looking into a concave and convex mirror help identify them?
Answer: You can distinguish between a concave mirror and a convex mirror without touching them. When you look into these mirrors by bringing your face close to each mirror, they will produce an image of your face of different types.

• A concave mirror will produce a magnified image of your face.
• A convex mirror will produce Diminished image of your face.

In simple words: If your reflection is bigger than you, the mirror is concave. If your reflection is smaller than you, the mirror is convex.

📝 Teacher's Note: This is a repetition of Solution 27, specifically focusing on the curved mirrors. It highlights their most distinct visual properties.

🎯 Exam Tip: "Magnified" and "Diminished" are the scientific keywords examiners look for here.

Page No: 262

Question 29. Illustrate the reflection of light in plane, convex, and concave mirrors with diagrams.
Answer:
In simple words: These diagrams show how rays of light bounce differently depending on whether the mirror is flat, curved out (convex), or curved in (concave).

📝 Teacher's Note: Point out how the rays "spread out" in a convex mirror and "come together" in a concave mirror. This explains why one is diverging and the other is converging.

🎯 Exam Tip: When drawing these, always use arrows to show the direction of light. The dashes on the mirror represent the non-reflecting side.

Question 30. State the uses of concave and convex mirrors.
Answer: Uses of concave mirror:

• Concave mirrors are used in reflecting microscope
• Concave mirrors are used in shaving and make up glasses.

Uses of convex mirror:

• Convex mirrors are used as a rear view mirror in automobiles as it provides a wider view of following traffic.

In simple words: Concave mirrors help us see tiny things bigger. Convex mirrors help us see more of the road behind us when driving.

📝 Teacher's Note: Mention that concave mirrors are also used by dentists to see enlarged images of teeth and in solar furnaces to concentrate sunlight.

🎯 Exam Tip: If an exam asks for "two uses," providing one for concave and one for convex is a common trap—make sure to provide what the specific mirror type requires.

Question 31. Why is our reflection clear on a polished table but unclear on an unpolished one?
Answer: We can see the reflection of our face on a polished table top because a regular reflection occurs in case of a polished surface while on a unpolished table top irregular reflection occurs which make image of our face unclear.
In simple words: A smooth table works like a mirror and bounces light in a neat way. A rough table scatters light in all directions, making the image look like a blur.

📝 Teacher's Note: Regular reflection happens on surfaces with microscopic smoothness. Irregular reflection happens when the surface has "hills and valleys" that scatter light rays.

🎯 Exam Tip: The scientific term for irregular reflection is "diffuse reflection." Using this term can gain you extra credit.

Question 32. State whether the following statements are TRUE or FALSE and provide the correct statement for false ones.
(a) The angle of incidence is the angle made by the incident ray with the plane mirror.
(b) If a ray of light incident on a plane mirror is such that it makes an angle of \( 30^\circ \) with the normal, then the angle of reflection is \( 60^\circ \).
(c) If the incident ray makes an angle of \( X^\circ \) with the normal, then the angle between the incident ray and reflected ray is \( 2X^\circ \).
(d) The image formed in a plane mirror is real, erect and same size as that of the object.
Answer:
(a) {FALSE}
Correct statement is the angle of incidence is the angle made by the incident ray with the normal to the surface of plane mirror.
(b) {FALSE}
Correct statement is if a ray of light incident on a plane mirror is such that it makes an angle of \( 30^\circ \) with the normal, then the angle of reflection is \( 30^\circ \).
(c) {TRUE}
(d) {FALSE}
Correct statement is the image formed in a plane mirror is virtual, erect and same size as that of the object.
In simple words: Angles are always measured from the "Normal" line, not the mirror itself. Also, mirrors show virtual (imaginary) images, not real ones.

📝 Teacher's Note: The most common student mistake in optics is measuring the angle from the mirror surface. Always remind them that the "Normal" is their reference point.

🎯 Exam Tip: For true/false questions, always read every word carefully. A single word like "real" instead of "virtual" makes the whole sentence false.

Question 33. State the laws of reflection and illustrate how a ray deviates.
Answer: Reflection obeys following two laws
a. The incident ray, the reflected ray, and the normal at the point of incidence, all lie in the same plane.
b. The angle of incidence and the angle of reflection are always equal.
According to these two laws this ray will deviate like this:
In simple words: Light hits a mirror and bounces off at the exact same angle on the other side of an imaginary vertical line.

📝 Teacher's Note: The "Normal" is a line drawn perpendicular (\( 90^\circ \)) to the reflecting surface at the point where the light hits it.

🎯 Exam Tip: In ray diagrams, always mark the "equal angles" with arc symbols and the same numerical value to show you understand the second law.

Question 34. How do two mirrors placed at an angle turn an incident ray?
Answer: Two planes when put in this way then they will turn the incident ray by \( 180^\circ \).
In simple words: If you place two mirrors at specific angles, they can bounce a light ray so that it ends up going exactly back the way it came.

📝 Teacher's Note: This setup is essentially how a "retro-reflector" works. It is used on bicycles and road signs to reflect car headlights directly back to the driver.

🎯 Exam Tip: A total deviation of \( 180^\circ \) means the final ray is antiparallel (exactly opposite) to the original ray.

Question 35. State the characteristics of an image formed by a plane mirror.
Answer: The image formed by a plane mirror is erect and virtual. It is a laterally inverted image. The image formed is of the same size as that of the object. Also, the image and the object are equidistant from the mirror.
In simple words: Your reflection is right-side up, exactly your size, as far away as you are, but your left and right are swapped.

📝 Teacher's Note: Lateral inversion means the left side of the object appears as the right side of the image. This is why "AMBULANCE" is written backward on the front of the vehicle.

🎯 Exam Tip: The four keywords for a plane mirror image are: "Virtual," "Erect," "Same size," and "Laterally Inverted."

Question 36. Show how lateral inversion depends on how an object is held relative to a mirror.
Answer:

(i) When the paper is held parallel to the mirror.
(ii) When the Paper is held perpendicular to the mirror.

In simple words: If you hold a word in front of a mirror, it looks backward. If you hold it sideways to the mirror, you might see it differently depending on your angle.

📝 Teacher's Note: Lateral inversion occurs in the direction perpendicular to the mirror's surface. When parallel, the text flips. When perpendicular, the top-to-bottom or front-to-back perspective changes.

🎯 Exam Tip: Drawing the letters of a word like "PLATE" in reverse is a great way to show you understand lateral inversion.

Question 37. If a boy is 3 m from a mirror, how far is he from his image? What if he moves to 4 m?
Answer: Given, distance of boy from the mirror \( = 3 \text{ m} \)

• Distance of image from mirror \( = \text{distance of boy from the mirror} = 3 \text{ m} \)
  Distance between boy and his image \( = \text{distance of boy from the mirror} + \text{distance of image from mirror} = 3 + 3 = 6 \text{ m} \)
• Now, distance of boy from the mirror \( = 4 \text{ m} \)
  Distance of image from mirror \( = 4 \text{ m} \)
  Distance between boy and his image \( = \text{distance of boy from the mirror} + \text{distance of image from mirror} = 4 + 4 = 8 \text{ m} \).

In simple words: In a mirror, your reflection is always as far behind the glass as you are in front of it. So the total gap is double your distance.

📝 Teacher's Note: This reinforces the "equidistant" property of plane mirrors. If you walk towards a mirror, your image walks toward you at the same speed.

🎯 Exam Tip: Be careful with wording—if the question asks for distance from the "mirror," it's one value; if from the "image," it's double that value.

Question 38. What is the use of a periscope?
Answer: Periscope is used to see over the top of an obstacle. It is also used in submarines for observing for movement of ships. It can be used from the trenches for observing the movement on the surface of earth.
In simple words: A periscope lets you see things that are higher up than you are, even if you are hiding behind a wall or underwater.

📝 Teacher's Note: A periscope works using two plane mirrors placed parallel to each other at a \( 45^\circ \) angle. It uses the principle of "successive reflections."

🎯 Exam Tip: "Submarines" and "trenches" are the two best real-world examples to mention for the use of a periscope.

Page No: 263

Question 39. Show how an eye observes an image after reflection from a plane mirror.
Answer: The image observed by the eye after reflection from a plane mirror can be completed as follows:
In simple words: Light hits the object, bounces off the mirror, and goes into your eye. Your brain "thinks" the light traveled in a straight line from behind the mirror, which is where you see the image.

📝 Teacher's Note: This diagram illustrates why we see a virtual image. The dotted lines show that the rays don't actually exist behind the mirror; our brain just extrapolates them.

🎯 Exam Tip: Always draw dotted lines for rays behind the mirror and solid lines for real rays in front of the mirror.

Question 40. Define the following parts of a spherical mirror: (a) Pole, (b) Centre of curvature, (c) Principal focus, (d) Principal axis, (e) Normal.
Answer:

• Pole is the centre of the reflecting surface, in this case spherical mirror.
• Centre of curvature is the centre of the imaginary sphere to which the mirror belongs.
• Principal focus of a spherical mirror is a point on the principal axis of the mirror, where all the rays travelling parallel to the principal axis and close to it after reflection from the mirror, converge to or appear to diverge from.
• Principal axis is the straight line passing through the pole and the centre of curvature.
• Focus of a concave mirror is a point on the principal axis of the mirror, where all the rays travelling parallel to the principal axis and close to it after reflection from the mirror converge to that point.
• Normal to the surface of a mirror at any point is the straight line at right angle to the tangent drawn at that point.

In simple words: These are the "labels" we use for different parts of a curved mirror so we can describe how light bounces off it precisely.

📝 Teacher's Note: Use a geometric circle to explain "normal." In a circle, any line from the center to the surface (the radius) is automatically a "normal" because it hits the surface at \( 90^\circ \).

🎯 Exam Tip: The definition of "Principal Focus" must mention "parallel to the principal axis" for it to be scientifically complete.

Question 41. (i) How many images are formed when mirrors are held perpendicular? (ii) What if they are parallel?
Answer: (i) When two mirrors are held perpendicular then number of images is 3 according to rule
Number of images \( = \frac{360}{X} - 1 \) if \( \frac{360}{X} \) is even.
Number of images is \( \frac{360}{90} - 1 = 4 - 1 = 3 \) images.
(ii) When two mirrors are held parallel to each other then, infinite numbers of image are formed.
In simple words: Two mirrors at a right angle show 3 copies. Two mirrors facing each other (like in a barbershop) show a never-ending line of reflections.

📝 Teacher's Note: This is a fun classroom experiment. Give two mirrors to students and ask them to count the images as they change the angle.

🎯 Exam Tip: If the question provides a different angle, just use the formula: \( \frac{360}{\text{angle}} - 1 \).

Question 42. Complete the path of the incident rays for the following cases in a concave mirror.
Answer: Completed path of the incident ray in following cases are:

(i) Ray hitting at an angle to the pole

(ii) Ray through focus

(iii) Ray through centre of curvature

In simple words: 1. At the center, it bounces at the same angle. 2. Through the focus, it bounces back straight. 3. Through the center of the sphere, it bounces exactly back where it came from.

📝 Teacher's Note: These are the "rules of ray construction." They are the most important tools for drawing any mirror diagram.

🎯 Exam Tip: Memorize the third case especially: a ray passing through \( C \) retraces its path. It's the easiest ray to draw!

Question 43. Show the image formation for an object placed at the centre of curvature in a concave mirror.
Answer: Position of image is exactly below the position of object as in this figure.
In simple words: If you place an object exactly at the center (\( C \)), the reflection will be the same size but upside down, right below the object.

📝 Teacher's Note: This is a unique case where the magnification is exactly \( -1 \). The distance of object (\( u \)) and image (\( v \)) from the pole are equal.

🎯 Exam Tip: Make sure the object and image touch the same vertical line at \( C \) to show they are at the same horizontal position.

Question 44. Show the image formation in a convex mirror.
Answer: Image formed is virtual, Dimished and erect.
In simple words: In a convex mirror, the reflection is always small, right-side up, and looks like it's behind the glass.

📝 Teacher's Note: "Diminished" is a scientific word for "smaller." This property is why convex mirrors are perfect for car side mirrors—they shrink the image to fit more of the road into the mirror.

🎯 Exam Tip: Note that for a convex mirror, the image is *always* between the pole and the focus.

Question 45. (i) Why does a convex mirror have a wider field of view? (ii) What happens if an object is at the focus of a concave mirror?
Answer: (i) In case of convex mirror all rays incident parallel to principal axis appear to diverge from a Focal point. So it has a wider field of view as it converge all rays to a single point.
(ii) In case of concave mirror if object is placed at Focal point then ray emerging from it after reflecting from mirror would be parallel to principal axis.
In simple words: (i) Convex mirrors spread rays out, making things look small and letting you see more. (ii) If you put a light at the focus point of a concave mirror, it will send out a perfectly straight beam of light (like a searchlight).

📝 Teacher's Note: The second part explains how car headlights and torches work—the bulb is placed at the focus to create a powerful straight beam.

🎯 Exam Tip: Concave mirrors "converge" light, and convex mirrors "diverge" light. Don't swap these terms!

Question 46. (i) Calculate the image position for a concave mirror with \( f = 25 \text{ cm} \) and \( u = 20 \text{ cm} \). (ii) What if the object is at \( 20 \text{ cm} \) but it is a convex mirror?
Answer: (i) Focal length \( = 25 \text{ cm} \). Object distance \( = 20 \text{ cm} \). Height of object \( = 10 \text{ cm} \).
Image is VIRTUAL, ERECT and MAGNIFIED.
(ii) Focal length \( = 25 \text{ cm} \). Object distance \( = 20 \text{ cm} \). Height of object \( = 10 \text{ cm} \).
Image is VIRTUAL, ERECT and DIMINISHED.
In simple words: (i) Because the object is very close (inside the focus), the concave mirror acts like a magnifying glass. (ii) The convex mirror always makes things smaller, no matter the distance.

📝 Teacher's Note: This is a great comparison. Both mirrors show a virtual, erect image, but one makes it huge and the other makes it tiny.

🎯 Exam Tip: Note that in Case (i), \( |u| < |f| \). This is the *only* case where a concave mirror produces a virtual image.

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Question 47. Calculate the nature of the image for a concave mirror with \( f = 10 \text{ cm} \) and object at \( 30 \text{ cm} \).
Answer: Focal length of concave mirror \( = 10 \text{ cm} \). Object distance \( = 30 \text{ cm} \).
Image is real, inverted and diminished.
In simple words: Since the object is quite far from the mirror (way past the center at 20 cm), the reflection is small and upside down.

📝 Teacher's Note: Object is at \( u = 3f \). This is beyond \( C \) (\( R = 20 \)). The resulting image will be between \( F \) and \( C \).

🎯 Exam Tip: If the object distance is more than twice the focal length, the image is always real, inverted, and diminished.

Question 48. Calculate the nature of the image for a mirror with \( f = 40 \text{ cm} \) and object height 5 cm at distance 30 cm.
Answer: Height of object \( = 5 \text{ cm} \). Distance of object \( = 30 \text{ cm} \). Focal length of mirror \( = 40 \text{ cm} \).
Image is virtual, erect and magnified.
In simple words: The object is closer than the focus (\( 30 \) is less than \( 40 \)), so the mirror magnifies it and shows it right-side up.

📝 Teacher's Note: This is the same principle as the makeup mirror. As long as you are "inside" the focal point, you get magnification.

🎯 Exam Tip: "Magnified" means the height of the image will be greater than \( 5 \text{ cm} \).

Question 49. (i) How is the centre of curvature determined? (ii) What is its value? (iii) Where is the focal length located? (iv) State the formula for focal length.
Answer:

• Centre of curvature can be determined by constructing the imaginary sphere to which lens belongs.
• Value of radius of curvature can be found by measuring the radius of this imaginary sphere geometrically.
• Focal length is the midpoint of pole and centre of curvature.
• focal length of mirror \( = \frac{\text{centre of curvature}}{2} \).

\( \implies \) Centre of curvature \( = 2.8 \text{ cm} \).
\( \implies \) Focal length of mirror \( = 1.4 \text{ cm} \).
\( \implies \) Focal length \( = \frac{\text{radius of curvature}}{2} \).
In simple words: The center of the "ball" is the center of curvature. The focal length is always exactly half that distance.

📝 Teacher's Note: Geometrically, any tangent to a circle is perpendicular to the radius. This property is used to determine the path of rays hit normally.

🎯 Exam Tip: The relationship \( f = R/2 \) is one of the most basic and important formulas in light and optics.

Question 50. Geometrically find the focal length if the centre of curvature is 4 cm.
Answer: Point F is Focus
OF \( = 2 \text{ cm} \)
OC \( = 4 \text{ cm} \)
F \( = 4/2 = 2 \text{ cm} \)
Focal length \( = 2 \text{ cm} \)
We know when incident ray is parallel to principal axis then they appear to diverge from a point F.
Geometrically we can find this value and this comes to \( 2 \text{ cm} \).
Centre of curvature \( = 4 \text{ cm} \).
Focal length \( = \frac{\text{centre of curvature}}{2} \).
In simple words: If the distance to the center is 4 cm, the focus point is right in the middle at 2 cm.

📝 Teacher's Note: In this geometry problem, 'O' is often used interchangeably with 'P' (Pole) to represent the origin on a scale.

🎯 Exam Tip: If an exam provides a diagram with a scale, always use the ruler tool to find these key points precisely.