Light – Reflection and Refraction — Practice

Question 1

Which mirror is used as a vehicle rear-view mirror and why?

Accepted Answer

Step 1 — A convex mirror; it always gives an erect, diminished image with a wide field of view.

✦ Answer: convex mirror, for a wider view.

Question 2

A concave mirror has radius of curvature 30 cm. Find its focal length.

Accepted Answer

Step 1 — f = R/2 = 30/2 = 15 cm (negative by convention: −15 cm).

✦ Answer: 15 cm (f = −15 cm).

Question 3

Find the power of a convex lens of focal length 25 cm.

Accepted Answer

Step 1 — f = 0.25 m; P = 1/0.25 = +4 D.

✦ Answer: +4 D.

Question 4

The speed of light in a medium is 2 × 10⁸ m/s. Find its refractive index (c = 3 × 10⁸ m/s).

Accepted Answer

Step 1 — n = c/v = (3×10⁸)/(2×10⁸).

Step 2 — n = 1.5.

✦ Answer: 1.5.

Question 5

An object is placed 20 cm from a concave mirror of focal length 10 cm. Find the image distance.

Accepted Answer

Step 1 — u = −20, f = −10. 1/v = 1/f − 1/u = −1/10 + 1/20 = −1/20.

Step 2 — v = −20 cm (real, in front of the mirror).

✦ Answer: v = −20 cm.

Question 6

A convex lens of focal length 10 cm forms an image of an object placed 15 cm away. Find v and the magnification.

Accepted Answer

Step 1 — u = −15, f = +10. 1/v = 1/f + 1/u = 1/10 − 1/15 = 1/30.

Step 2 — v = +30 cm (real image on the other side).

Step 3 — m = v/u = 30/(−15) = −2 (real, inverted, magnified twice).

✦ Answer: v = 30 cm, m = −2.

Question 7

An object is 10 cm from a concave mirror of focal length 15 cm. Find the image position and nature.

Accepted Answer

Step 1 — u = −10, f = −15. 1/v = 1/f − 1/u = −1/15 + 1/10 = 1/30.

Step 2 — v = +30 cm (behind the mirror ⇒ virtual).

Step 3 — m = −v/u = −30/(−10) = +3 (erect, magnified 3×).

✦ Answer: virtual, erect, magnified image 30 cm behind the mirror.

Question 8

Two lenses of powers +5 D and −2 D are placed in contact. Find the power and focal length of the combination.

Accepted Answer

Step 1 — P = P₁ + P₂ = 5 + (−2) = +3 D.

Step 2 — f = 1/P = 1/3 m ≈ 33.3 cm (converging).

✦ Answer: +3 D, f ≈ 33.3 cm.

Question 9

An object is 15 cm from a convex mirror of focal length 10 cm. Find the image distance.

Accepted Answer

Step 1 — u = −15, f = +10. 1/v = 1/f − 1/u = 1/10 + 1/15 = 1/6.

Step 2 — v = +6 cm (virtual, behind the mirror).

✦ Answer: v = +6 cm (virtual, erect, diminished).

Question 10

State the nature of the image when an object is placed between the pole and focus of a concave mirror.

Accepted Answer

Step 1 — The image is virtual and erect.

Step 2 — It is enlarged and forms behind the mirror.

✦ Answer: virtual, erect and magnified (behind the mirror).

Practice — Light – Reflection and Refraction

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