Frank Brothers Solutions for ICSE Class 9 Physics Chapter 6.2 Light Spherical Mirrors

Page No: 258

Question 1. Define a spherical mirror.
Answer: A spherical mirror is a part of a hollow glass sphere silvered on one side.
In simple words: Imagine a hollow glass ball. If you cut out a piece of it and coat one side with silver, you get a spherical mirror.

📝 Teacher's Note: Use a shiny metal spoon as a real-life example. The inside of the spoon acts like a concave mirror, while the back acts like a convex mirror.

🎯 Exam Tip: Remember to mention "hollow glass sphere" and "silvered on one side" for a complete definition.

Question 2. Explain the principal focus of a concave mirror with a diagram.
Answer: The parallel beam of light on reflection by a concave mirror converges at a point on the principal axis, midway between pole and the centre of curvature. This point is called principal focus.
In simple words: When straight rays of light hit a concave mirror, they all bounce back and meet at one single spot in the middle. This spot is the Focus.

📝 Teacher's Note: Explain "converging" as "coming together." This is why concave mirrors are used in solar cookers to concentrate sunlight.

🎯 Exam Tip: Always mark the arrows on your rays to show the direction of light. A ray diagram without arrows is technically incorrect.

Question 3. If the radius of curvature of a mirror is 30 cm, find its focal length.
Answer: \( \text{Focal length} = \frac{1}{2} \text{ of radius of curvature} \)
\( \implies \text{Focal length} = \frac{1}{2} \times 30 = 15 \text{ cm} \).
In simple words: The focal length is always exactly half the distance of the radius. So, half of 30 is 15.

📝 Teacher's Note: Use the formula \( f = \frac{R}{2} \). It is one of the most common numerical questions for this chapter.

🎯 Exam Tip: Don't forget to write the unit (cm) in your final answer.

Question 4. What is the focal point?
Answer: Focal point is the principal focus of the mirror where a parallel beam of light meets (or appear to meet) after reflection from the mirror.
In simple words: It is the specific point where all incoming straight light rays collect after bouncing off the mirror.

📝 Teacher's Note: Emphasize "meets" for concave mirrors and "appears to meet" for convex mirrors.

🎯 Exam Tip: "Principal focus" and "focal point" mean the same thing in this context.

Question 5. State the differences between real and virtual images.
Answer:

In simple words: A real image is upside down and can be caught on a piece of paper (like a movie screen). A virtual image is right-side up and only "looks" like it is behind the mirror.

📝 Teacher's Note: A cinema screen shows real images, while the reflection you see in your bathroom mirror is a virtual image.

🎯 Exam Tip: The ability to be "obtained on a screen" is the most important distinction for examiners.

Question 6. Define the following terms: (i) Pole, (ii) Centre of curvature, (iii) Aperture, (iv) Principal axis, (v) Principal focus.
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.
• Aperture is the distance between the extreme points on the periphery of the mirror.
• Principal axis is the straight line passing through the pole and the centre of curvature.
• The principle focus of a spherical mirror may be defined as a point on its principle axis where a beam of light parallel to the principle axis converges to or appears to diverge from after reflection from the spherical mirror.

In simple words: The Pole is the mirror's belly-button. The Centre of Curvature is the center of the ball the mirror was cut from. The Principal Axis is the main road going through both.

📝 Teacher's Note: Use a diagram to show all these points simultaneously. It helps students understand the spatial relationships between them.

🎯 Exam Tip: For Aperture, think of it as the "size" or "width" of the mirror's opening.

Question 7. Which mirror has a wider field of view?
Answer: Convex mirror has a wider field of view.
In simple words: A convex mirror is curved outward, so it can "see" much more of the area behind it than a flat or concave mirror.

📝 Teacher's Note: This is why convex mirrors are used in car side-view mirrors—they show you more lanes of traffic.

🎯 Exam Tip: "Wider field of view" is the key phrase needed to explain why convex mirrors are used as safety mirrors.

Question 8. 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 to see tiny things or in mirrors to make your face look bigger when shaving or applying makeup.

📝 Teacher's Note: Concave mirrors magnify things when they are held close, which is perfect for seeing details on the skin or inside an eye.

🎯 Exam Tip: Shaving mirrors and solar cookers are the most commonly asked examples in exams.

Question 9. Why are convex mirrors used as rear view mirrors in automobiles?
Answer: Convex mirrors are used as a rear view mirror in automobiles as it provides a wider view of following traffic.
In simple words: They let the driver see a larger part of the road behind the car, helping them drive more safely.

📝 Teacher's Note: Mention that the images in a convex mirror are always smaller, which is why there's often a warning: "Objects in the mirror are closer than they appear."

🎯 Exam Tip: Always relate the "use" to the "property" (wide field of view + diminished erect image).

Question 10. Which mirror is used in vehicles to see the traffic following it?
Answer: Convex mirror is used in vehicles to see the traffic following it.
In simple words: The side mirrors and center mirrors in cars are convex mirrors.

📝 Teacher's Note: This is a direct application question. It checks if the student can apply theoretical knowledge to real-world objects.

🎯 Exam Tip: If the question asks "why," combine this answer with the "wide field of view" point from Question 9.

Question 11. State the relationship between focal length and radius of curvature.
Answer: The relationship between the focal length, \( f \) and radius of curvature, \( r \) is \( f = \frac{1}{2} \times r \).
In simple words: The focus point is always exactly halfway between the mirror and the center of its curve.

📝 Teacher's Note: Make sure students don't confuse the two—\( f \) is the smaller distance, \( r \) is the larger one. So \( R = 2f \).

🎯 Exam Tip: This formula is valid only for mirrors with small apertures.

Question 12. Describe the image formed by a concave mirror when the object is at the centre of curvature.
Answer: A concave mirror forms a real image equal in size to the object when the object is kept at centre of curvature, C.
In simple words: If you place an object exactly at the center (C), the reflection will be the same size but upside down, right beneath the object.

📝 Teacher's Note: This is a unique case where the object and image are at the same position and have the same size. Magnification is \( -1 \).

🎯 Exam Tip: When drawing this, ensure the image is exactly as tall as the object to show they are "equal in size."

Question 13. Describe the image formed by a concave mirror when the object is between focus and pole.
Answer: A concave mirror forms an enlarged virtual image when the object is kept between focus, F and pole, P.
In simple words: When the object is very close to the mirror, you see a giant, right-side-up image that looks like it is "inside" the mirror.

📝 Teacher's Note: This is the case used for shaving and makeup mirrors. The image is magnified and erect, which is very helpful.

🎯 Exam Tip: Virtual images should always be drawn using "dotted lines" to show they are not formed by actual ray intersection.

Question 14. Which mirror produces a real and diminished image of an object?
Answer: Concave mirror can produce real and diminished image of the object.
In simple words: When the object is far away from a concave mirror, its reflection is small and upside down.

📝 Teacher's Note: This happens when the object is beyond the Centre of Curvature (C). The image is formed between C and F.

🎯 Exam Tip: Note that convex mirrors also produce diminished images, but they are *always* virtual, not real.

Question 15. 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 has no curve, its center would be infinitely far away. So its focal point is also at infinity.

📝 Teacher's Note: A plane mirror can be thought of as a spherical mirror with an infinitely large radius.

🎯 Exam Tip: "Infinity" is the one-word answer examiners expect for this common factual question.

Question 16. Where should an object be placed to obtain a magnified and erect image using a concave mirror?
Answer: The object should be placed between F and P to obtain its magnified and erect image.
In simple words: You have to hold the object very close to the mirror (closer than the focus point) to see it right-side up and bigger.

📝 Teacher's Note: This is the only position for a concave mirror that produces a virtual, erect, and magnified image.

🎯 Exam Tip: Mentioning the specific region "between Focus (F) and Pole (P)" is essential for full marks.

Question 17. Prove that for a spherical mirror, \( 2f = R \).
Answer: Let’s assume the aperture of the mirror to be very small. Let a ray AB of light parallel to the principal axis be incident on the concave mirror at B. The ray makes the angle of incidence, \( i \) with the normal BC at B, C being the centre of curvature of the mirror. The ray is reflected along BF with angle of reflection, \( r \) so that
\( i = r \)
In accordance with the laws of reflection. As the incident ray AB is parallel to the principal axis PC, so the reflected ray BF passes through the principal focus, F. In figure (i)
\( \angle ABC = \angle CBF \)
But \( \angle ABC = \text{alternate } \angle BCF \)
Therefore \( \angle CBF = \angle BCF \)
And the \( \triangle FBC \) is isosceles
BF = FC ...(i)
Since the aperture is assumed to be very small, so the point of incidence B is close to P
And BF \( \approx \) PF (approx.) ...(ii)
From (i) and (ii)
PF = FC
Adding PF to both sides
PF + PF = PF + FC
2PF = PC
Now since PF = \( f \), the focal length of the mirror
And PC = R, the radius of curvature of the mirror
Therefore 2\( f \) = R

\( \implies \) From here we can determine the focal length of the concave mirror i.e. half of radius of curvature.
In simple words: By using geometry and the laws of reflection, we can prove that the focus point is exactly in the middle of the distance from the mirror to the center.

📝 Teacher's Note: This geometric derivation is a favorite long-answer question. Focus on the alternate angles and the isosceles triangle properties.

🎯 Exam Tip: Clearly state the assumption that "the aperture of the mirror is very small" at the beginning of your proof.

Question 18. 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 = height of image / height of object.
In simple words: Magnification tells you how many times bigger or smaller the reflection is compared to the real thing. Positive means right-side up; negative means upside down.

📝 Teacher's Note: Magnification \( m = \frac{h_i}{h_o} \). If \( |m| > 1 \), the image is enlarged; if \( |m| < 1 \), it is diminished.

🎯 Exam Tip: Remember: Real is Negative (RN) and Virtual is Positive (VP). This helps in keeping the signs correct.

Question 19. What is the SI unit of focal length?
Answer: SI unit of focal length is meter.
In simple words: Like any other distance in science, focal length is officially measured in meters.

📝 Teacher's Note: While we use cm for school problems, the official Standard International (SI) unit is always the meter.

🎯 Exam Tip: "Meter" is the correct SI unit, but don't lose marks by not converting your cm to m if the question specifically asks for SI units.

Question 20. In a composite mirror where the top is convex, middle is concave, and bottom is plane, identify the mirror types.
Answer: The top mirror is convex mirror, the middle mirror is concave mirror and bottom mirror is a plane mirror.
In simple words: This is like a "magic mirror." Each section changes how you look because they are different types of mirrors stacked together.

📝 Teacher's Note: This is sometimes called a "Laughing Mirror." The convex part makes you look wide/far, the concave part can flip you or magnify you, and the plane part shows you as you are.

🎯 Exam Tip: Match the property of the reflection (e.g., smaller, bigger, or same size) to the specific mirror type.

Question 21. Why is a mirror with focal length +15 cm identified as convex?
Answer: The mirror having +15 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 because their focus point is "behind" the mirror on the positive side of the graph.

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

🎯 Exam Tip: Memorize: Convex focus is positive (+), Concave focus is negative (-).

Question 22. Why is a mirror with focal length -20 cm identified as concave?
Answer: The mirror having -20 cm as its focal length is a concave mirror because focal length is taken negative only in case of concave mirror.
In simple words: The minus sign tells us it's a concave mirror because its focus is in front of the mirror.

📝 Teacher's Note: Just like Question 21, this is an application of sign conventions. Negative focal length always indicates a converging (concave) mirror.

🎯 Exam Tip: Always look at the sign (+/-) of the focal length given in a problem to identify the mirror type immediately.

Question 23. Why is the image of our face in a plane mirror called virtual?
Answer: When we look into a plane mirror, the image of our face is virtual because the image cannot be obtained on a screen.
In simple words: If you put a piece of paper where your reflection "is," you won't see anything on the paper. The image only exists in your eyes.

📝 Teacher's Note: Use the term "imaginary" as a conceptual aid, but always use "virtual" in scientific writing.

🎯 Exam Tip: The standard definition of a virtual image is that it cannot be projected onto a screen.

Question 24. Describe how the image changes when an object is moved towards a concave mirror.
Answer: When an object is brought towards the concave mirror, the position of the image moves away from the mirror and the size increases and it remains inverted but at object position between F and P, the image is virtual, magnified and erect.
In simple words: As you move closer, your upside-down reflection gets bigger and moves back. But once you cross a certain point (F), you suddenly see a huge right-side-up image.

📝 Teacher's Note: This is a great way to summarize all concave mirror cases in one sentence. It captures the transition from real to virtual images.

🎯 Exam Tip: Be sure to distinguish between the behavior *outside* the focus and *inside* the focus.

Question 25. Draw a ray diagram for a virtual, erect, and diminished image formed by a spherical mirror.
Answer:
A light ray coming from a point on object AB is reflected from the surface of the mirror. When this ray is produced backwards, it passes through the principal focus and the ray which traces its incident path after reflection, when produced backwards, passes through the centre of curvature. These two reflected rays coincide at a point where the image is formed. The image, A’B’ is virtual, erect, and diminished in size. The focal length was found to be 24 mm.
In simple words: This is how a convex mirror works. It always makes things look smaller and right-side up, which is why you can see so much behind you in a car's side mirror.

📝 Teacher's Note: Convex mirrors are also called "diverging mirrors" because they spread light rays apart.

🎯 Exam Tip: For a convex mirror, remember the image is *always* virtual, erect, and smaller than the object, no matter where you put it.

Page No: 259

Question 26. Show the formation of a real, inverted, and diminished image by a concave mirror.
Answer: A light ray coming from a point on object AB is reflected from the surface of the mirror, it passes through the principal focus and the other ray passing through the centre of curvature strikes the mirror normally i.e. 90 degree. Hence it will reflect back. These two reflected rays coincide at a point where the image is formed. The image, A’B’ is real, inverted, and diminished in size. The focal length was found to be 16 mm.
In simple words: If you are far from a concave mirror, your reflection will be small and upside down in front of the mirror.

📝 Teacher's Note: This occurs when the object is placed beyond the Centre of Curvature. The image is "real" because the rays actually meet.

🎯 Exam Tip: "Normally" means at a 90-degree angle. Any ray going through C hits the mirror at 90 degrees and bounces straight back.

Question 27. Draw ray diagrams showing rays through Focus (F) and Centre of Curvature (C) for both concave and convex mirrors.
Answer:
A light ray when produced backwards passes through principal focus as shown in the problem figure. We draw the normal through centre of curvature at the point of incidence and draw the reflected ray at an angle equal to the angle of incidence thus following the laws of reflection. The reflected ray is parallel to the principal axis. The other ray is reflected at the pole by an angle in accordance with the laws of reflection. These two reflected rays when produced backwards coincide at a point where the image is formed. The image, A’B’ is virtual, erect, and diminished in size.
In simple words: This shows the rules of how light bounces. A ray going toward the focus bounces back straight (parallel).

📝 Teacher's Note: These are the standard "rules of ray construction." There are four such rules, and you need at least two to find an image position.

🎯 Exam Tip: Memorize this: Parallel rays go through Focus; rays through Focus become Parallel.

Question 28. Describe the formation of a virtual image in a convex mirror.
Answer A light ray when produced backwards passes through principal focus as shown in the problem figure. We draw the normal through centre of curvature at the point of incidence and draw the reflected ray at an angle equal to the angle of incidence thus following the laws of reflection. The reflected ray is parallel to the principal axis. The other ray is passing through the centre of curvature as shown in problem figure. This ray retraces its incident path because it strikes the mirror normally i.e. 90 degrees. These two reflected rays when produced backwards coincide at a point where the image is formed. The image, A’B’ is virtual, erect, and diminished in size.
In simple words: Since convex mirrors bend outward, they spread light out. To find where the image is, we have to trace the rays backwards "inside" the mirror.

📝 Teacher's Note: This is a common point of confusion—convex mirrors never form real images. The reflection is always "behind" the mirror surface.

🎯 Exam Tip: Whenever a ray hits the mirror "normally" (along the radius), it bounces exactly back the way it came. This is a very useful rule to use in drawings.

Question 29. Show the formation of a real, inverted, and diminished image by a concave mirror when the object is at a specific distance.
Answer: A light ray, parallel to the principal axis, coming from a point on object AB is reflected from the surface of the mirror, it passes through the principal focus and the other ray passing through the centre of curvature strikes the mirror normally i.e. 90 degree. Hence it will reflect back. These two reflected rays coincide at a point between F and C, where the image is formed. The image, A’B’ is real, inverted, and diminished in size.
In simple words: This happens when the object is far away from the mirror. The reflection is a tiny, upside-down version that stays close to the focus.

📝 Teacher's Note: This is the case for a very distant object, like a tree or building seen in a concave mirror. The image will be small and real.

🎯 Exam Tip: Diminished means "smaller." Inverted means "upside down." These terms are essential for describing image nature.

Question 30. Describe the formation of a virtual, erect, and magnified image in a concave mirror.
Answer: A light ray, parallel to the principal axis, coming from a point on object AB is reflected from the surface of the mirror, it passes through the principal focus and the other ray striking normally to the mirror reflects back and passes through the centre of curvature. These two reflected rays, when produced backwards, coincide at a point where the image is formed. The image, A’B’ is virtual, erect, and magnified in size.
In simple words: This is the "makeup mirror" effect. When you are very close, you see your face much bigger and right-side up.

📝 Teacher's Note: Magnified means "larger." This is the only case where a concave mirror produces an erect (upright) image. It is extremely important for students to remember this special case.

🎯 Exam Tip: If an image is virtual, it must always be erect. If an image is real, it must always be inverted. These pairs (Virtual-Erect and Real-Inverted) almost always go together.