CBSE Class 10 Physics Light Reflection and Refraction MCQs Set 12

Answer: (b) radius of curvature

Explanation:
1. The radius of the sphere of which the mirror is a part is the radius of curvature, R.
2. The centre of that sphere is the centre of curvature C.

Teacher's Note:
1. Radius of curvature R = PC.
2. R = 2f for small apertures.

Answer: (c) I–S, II–R, III–Q, IV–P

Explanation:
1. A plane mirror shows lateral inversion (I–S).
2. A real image can be taken on a screen (II–R).
3. A virtual image cannot be taken on a screen (III–Q).
4. A convex mirror always forms a virtual image (IV–P).

Teacher's Note:
1. Match each term with its defining property.
2. Real: on screen; virtual: not on screen.

Answer: (b) 90°

Explanation:
1. Two plane mirrors at 90° form a corner reflector.
2. Whatever the angle of incidence, the ray after two reflections is antiparallel to the incident ray.

Teacher's Note:
1. The angles of incidence at the two mirrors add up to 90°.
2. This is the principle of a corner reflector.

Answer: (c) 36°

Explanation:
1. For a symmetric object, n = (360°/θ) − 1.
2. 9 = (360°/θ) − 1, so 360°/θ = 10.
3. θ = 360°/10 = 36°.

Teacher's Note:
1. Rearrange the formula to θ = 360°/(n + 1).
2. Check: 360°/36° − 1 = 9.

Answer: (c) + 0.5

Explanation:
1. u = −60 cm and v = +30 cm (behind the mirror).
2. m = −v/u = −(+30)/(−60) = +0.5.
3. The positive sign shows that the image is virtual and erect.

Teacher's Note:
1. Image behind the mirror means positive v.
2. A positive m less than 1 is typical of a convex mirror.

Answer: (a) + 5.0

Explanation:
1. f = −25 cm and u = −20 cm.
2. Mirror formula: 1/v = 1/f − 1/u = −1/25 + 1/20 = 1/100, so v = +100 cm (behind the mirror).
3. m = −v/u = −(100)/(−20) = +5.

Teacher's Note:
1. The object is inside the focus (20 cm < 25 cm), so the image is virtual, erect and magnified.
2. The positive sign of m matches this.

Answer: (b) 1.0 × 10² cm behind the mirror

Explanation:
1. 1/v + 1/u = 1/f gives 1/v = −1/25 + 1/20 = 1/100.
2. v = +100 cm = 1.0 × 10² cm.
3. The positive sign means the image is behind the mirror (virtual).

Teacher's Note:
1. When the object is between the pole and the focus of a concave mirror, the image is behind the mirror.
2. Check the sign of v after calculating.

Answer: (b) 60°

Explanation:
1. n = (360°/θ) − 1 = 5, so 360°/θ = 6.
2. θ = 360°/6 = 60°.

Teacher's Note:
1. Use θ = 360°/(n + 1).
2. Check: 360°/60° − 1 = 5.

Answer: (b) 30 cm in front of the mirror

Explanation:
1. Sun's rays are parallel, so the point where they converge is the focus: f = 15 cm.
2. The image is the same size when the object is at the centre of curvature.
3. C is at R = 2f = 2 × 15 = 30 cm in front of the mirror.

Teacher's Note:
1. Image of the sun gives the focal length.
2. Same size image needs the object at C = 2f.

Answer: (b) − 20 cm

Explanation:
1. The image is real and inverted, so m = −5/10 = −0.5, and v = −30 cm.
2. m = −v/u gives −0.5 = 30/u, so u = −60 cm.
3. 1/f = 1/v + 1/u = −1/30 − 1/60 = −3/60, so f = −20 cm.

Teacher's Note:
1. First get u from the magnification, then use the mirror formula.
2. A concave mirror always has a negative focal length.

Answer: (c) 7

Explanation:
1. n = (360°/θ) − 1 = (360°/45°) − 1 = 8 − 1 = 7.

Teacher's Note:
1. Substitute directly into n = 360°/θ − 1.
2. 45° is a divisor of 360°, so the answer is a whole number.

Answer: (b) 36 cm away from the mirror

Explanation:
1. First position: u = −40 cm, f = −15 cm: 1/v = −1/15 + 1/40 = −5/120, so v₁ = −24 cm.
2. After moving 20 cm: u = −20 cm: 1/v = −1/15 + 1/20 = −1/60, so v₂ = −60 cm.
3. The image moves from 24 cm to 60 cm from the mirror, i.e. 36 cm away from it.

Teacher's Note:
1. Apply the mirror formula twice and subtract the image distances.
2. The image moves away from the mirror as the object nears the focus.

Answer: (a) +24 cm

Explanation:
1. u = −40 cm and v = +15 cm (behind the mirror).
2. 1/f = 1/v + 1/u = 1/15 − 1/40 = (8 − 3)/120 = 1/24.
3. f = +24 cm. The focal length of a convex mirror is positive.

Teacher's Note:
1. A convex mirror always has a positive focal length.
2. Always check the sign of f against the type of mirror.

Answer: (d) At 30 cm in front of the mirror

Explanation:
1. f = −10 cm and u = −15 cm.
2. 1/v = 1/f − 1/u = −1/10 + 1/15 = −1/30.
3. v = −30 cm, i.e. the image is 30 cm in front of the mirror (real).

Teacher's Note:
1. Object between F and C gives a real image beyond C.
2. Negative v means in front of the mirror.

Answer: (c) At a distance of 10 cm behind the mirror

Explanation:
1. f = +20 cm (convex mirror) and u = −20 cm.
2. 1/v = 1/f − 1/u = 1/20 + 1/20 = 1/10.
3. v = +10 cm, i.e. 10 cm behind the mirror.

Teacher's Note:
1. A convex mirror always forms its image behind it, within f.
2. Here v = 10 cm < f = 20 cm.

Answer: (b) 4 ms⁻¹

Explanation:
1. The image moves towards the mirror at 2 m/s while the man moves towards the mirror at 2 m/s from the other side.
2. Relative speed = 2 + 2 = 4 m/s.

Teacher's Note:
1. Object and image approach each other, so add the speeds.
2. The image speed equals the object speed.

Answer: (b) 4 cm

Explanation:
1. Originally the image is 20 cm behind the mirror, i.e. 40 cm from the object.
2. After the mirror moves 2 cm towards the object, the object is 18 cm from the mirror and the image is 18 cm behind it, i.e. 36 cm from the object.
3. The image has therefore shifted by 40 − 36 = 4 cm.

Teacher's Note:
1. If a plane mirror moves by d, the image moves by 2d.
2. The object is fixed, so the whole shift comes from the mirror.

Answer: (b) 10 cm

Explanation:
1. f = R/2 = 20/2 = 10 cm.

Teacher's Note:
1. Focal length is always half the radius of curvature.
2. Sign depends on the type of mirror.

Answer: (c) 10 cm

Explanation:
1. For a virtual image m = +2 and f = −20 cm.
2. m = f/(f − u) gives 2 = −20/(−20 − u), so −20 − u = −10 and u = −10 cm.
3. The object must be 10 cm from the mirror, within the focus.

Teacher's Note:
1. Virtual image from a concave mirror: object inside the focus.
2. Check: v = 20 cm behind the mirror.

Answer: (d) 75 cm

Explanation:
1. An inverted image means m = −2 and f = −50 cm.
2. m = f/(f − u) gives −2 = −50/(−50 − u), so −50 − u = 25 and u = −75 cm.
3. The object must be at 75 cm.

Teacher's Note:
1. Inverted means real, so the object lies between F and C.
2. Here F = 50 cm and C = 100 cm; 75 cm lies between them.

Answer: (c) +1.0 cm

Explanation:
1. A diverging mirror is convex: f = +10 cm and u = −30 cm.
2. 1/v = 1/f − 1/u = 1/10 + 1/30 = 4/30, so v = +7.5 cm.
3. m = −v/u = 7.5/30 = 0.25, so h′ = 0.25 × 4 = +1.0 cm.

Teacher's Note:
1. A convex mirror gives an erect, diminished image, so the height is positive and less than 4 cm.
2. Check m = f/(f − u) = 10/40 = 0.25.

Answer: (d) At 60 cm infront of the mirror

Explanation:
1. f = −20 cm and u = −30 cm.
2. 1/v = 1/f − 1/u = −1/20 + 1/30 = −1/60, so v = −60 cm.
3. The image is 60 cm in front of the mirror (real and inverted).

Teacher's Note:
1. The object is between F and C, so the image is beyond C.
2. Here C is at 40 cm and the image is at 60 cm.

Answer: (a) 22%

Explanation:
1. v = +0.78 m and u = −3.5 m.
2. m = −v/u = 0.778/3.5 = 0.222.
3. So the image is about 22% of the size of the truck.

Teacher's Note:
1. Magnification of 0.22 means 22% of the actual size.
2. Convert m into a percentage by multiplying by 100.

Answer: (a) −80 cm

Explanation:
1. The image is real and inverted, so h′ = −4 cm and m = −4/1 = −4.
2. m = −v/u gives −4 = −v/(−20), so v = −80 cm.

Teacher's Note:
1. A converging mirror is a concave mirror, and real images are in front of it, so v is negative.
2. The image distance is four times the object distance.

Answer: (b) 16 cm

Explanation:
1. u = −20 cm and v = −80 cm.
2. 1/f = 1/v + 1/u = −1/80 − 1/20 = −5/80 = −1/16.
3. So f = −16 cm, and its magnitude is 16 cm.

Teacher's Note:
1. A concave mirror has a negative focal length.
2. Always give the magnitude when asked for it.

Answer: (c) 1/3

Explanation:
1. f = +f and u = −2f.
2. 1/v = 1/f + 1/(2f) = 3/(2f), so v = 2f/3.
3. m = −v/u = (2f/3)/(2f) = 1/3.

Teacher's Note:
1. A convex mirror always gives m between 0 and 1.
2. Check: m = f/(f − u) = f/(3f) = 1/3.

Answer: (d) A is false, but R is true.

Explanation:
1. The focal length of a mirror is f = R/2, which depends only on the radius of curvature.
2. It does not change when the mirror is placed in water, so Assertion is false.
3. Reason is true.

Teacher's Note:
1. Mirrors reflect light, so the surrounding medium does not matter.
2. Lenses refract, so their focal length does change in a liquid.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. By the Cartesian sign convention, a convex mirror has positive f and a concave mirror has negative f.
2. Both statements are true, but the second does not explain the first.

Teacher's Note:
1. Both signs come from the same sign convention.
2. One does not cause the other.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. A convex mirror gives a diminished image, so a tall building fits in it: A is true.
2. The laws of reflection hold for all mirrors: R is true.
3. R is not the reason why the full image is seen (that is because of diminished images and a wide field of view).

Teacher's Note:
1. Diminished image and wide field of view explain the assertion.
2. The laws of reflection are a separate fact.

Answer: (c) A is true, but R is false.

Explanation:
1. u = −26 cm and f = +26 cm, so 1/v = 1/26 + 1/26 = 1/13 and v = +13 cm.
2. The image is formed at 13 cm behind the mirror, not at infinity, so A is true.
3. The equation does not give v = ∞, so R is false.

Teacher's Note:
1. An image at infinity needs u = f for a concave mirror.
2. For a convex mirror the image is always at a finite distance.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. A concave mirror makes parallel sunlight converge at its focus.
2. The concentrated light produces a high temperature at the focus.
3. Both are true and R explains A.

Teacher's Note:
1. Solar furnaces and cookers use concave mirrors.
2. Convergence of light means concentration of energy.

Answer: (c) A is true, but R is false.

Explanation:
1. A ray along the normal strikes the mirror at 0° to the normal, so ∠i = ∠r = 0° and the ray retraces its path: A is true.
2. The angle of incidence is 0°, not π/2, so R is false.

Teacher's Note:
1. Angle of incidence is measured from the normal.
2. A ray along the normal has ∠i = 0.

Answer: (d) A is false, but R is true.

Explanation:
1. The focal length of a mirror does not depend on the medium, so A is false.
2. f = R/2 for a spherical mirror, so R is true.

Teacher's Note:
1. Do not confuse mirrors with lenses.
2. Only lenses change focal length in a different medium.

Answer: (c) A is true, but R is false.

Explanation:
1. Convex mirrors give a wide field of view and erect, diminished images, so they are used as rear-view mirrors: A is true.
2. The image is diminished, not the same size, so R is false.

Teacher's Note:
1. Only a plane mirror gives the same size image.
2. A convex mirror gives a smaller image.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. The word is written laterally inverted so that the driver in front reads it correctly in the rear-view mirror: A is true.
2. A plane mirror image is the same size as the object: R is true.
3. The same size is not the reason for writing the word laterally inverted.

Teacher's Note:
1. The image in a mirror is laterally inverted, not just the same size.
2. Writing it reversed makes it readable in the mirror.

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. A ray through C falls along a radius, i.e. along the normal, so i = r = 0° and it retraces its path: A is true.
2. The coplanarity of incident ray, reflected ray and normal is the second law of reflection: R is true.
3. But it is not the reason for the retracing.

Teacher's Note:
1. The ray retraces its path because it falls along the normal.
2. Both statements are laws or consequences of reflection.

Answer: (c) A is true, but R is false.

Explanation:
1. A convex mirror is used as a rear-view mirror because it gives a wide field of view and erect images: A is true.
2. The images of vehicles are diminished, not larger than actual size, so R is false.

Teacher's Note:
1. A convex mirror always gives diminished images.
2. The field of view is large because the images are small.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. A plane mirror forms an erect, virtual image of the same size, so m = +1: A is true.
2. R states exactly why: virtual (positive sign) and same size (value 1).

Teacher's Note:
1. m = +1 means same size and erect.
2. It is the only mirror with m = +1 for every object position.

Answer: (c) A is true, but R is false.

Explanation:
1. A plane mirror forms only virtual images of real objects: A is true.
2. A convex mirror always forms a virtual image, so R is false.

Teacher's Note:
1. Convex mirror: always virtual, erect and diminished.
2. Real images need a concave mirror or a convex lens.

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. A real image is formed below the principal axis, so its height is negative and m is negative.
2. A real image is inverted, which is the reason for the negative sign.

Teacher's Note:
1. Inverted image means negative height.
2. Hence negative magnification.