Chapter 9: Light – Reflection and Refraction

Q1: (d) Clay (opaque). Q2: (d) Between the pole and focus (concave mirror → virtual, erect, magnified). Q3: (b) At 2F (real image, same size). Q4: (a) both concave (f = −15 cm → concave mirror & concave lens). Q5: (d) either plane or convex. Q6: (c) a convex lens of focal length 5 cm (magnifying glass).

For an erect image with a concave mirror, the object must be placed between the pole and the focus (0 to 15 cm). The image is virtual, erect and larger (magnified) than the object, formed behind the mirror.

(a) Headlights → concave mirror (bulb at focus gives a strong parallel beam). (b) Side/rear-view → convex mirror (gives an erect, diminished image and a wider field of view). (c) Solar furnace → concave mirror (concentrates sunlight at the focus to produce great heat).

Yes, it still forms a complete image, because rays from every part of the object still pass through the uncovered half and converge to form the full image. However, the image is less bright (dimmer) since less light passes through.

u = −25 cm, f = +10 cm. 1/v = 1/f + 1/u = 1/10 − 1/25 = (5−2)/50 = 3/50 → v = +16.7 cm (real, on the other side). m = v/u = 16.7/(−25) = −0.67 → h′ = −0.67 × 5 = −3.3 cm. So the image is real, inverted and diminished (~3.3 cm), ~16.7 cm from the lens.

Q11: f=−15, v=−10. 1/u = 1/v − 1/f = −1/10 + 1/15 = (−3+2)/30 = −1/30 → u = −30 cm (object 30 cm from lens). Q12: Convex mirror f=+15, u=−10. 1/v = 1/f − 1/u = 1/15 + 1/10 = 5/30 → v = +6 cm — image is virtual, erect, diminished, 6 cm behind the mirror.

Q13: m = +1 means the image is the same size as the object (|m|=1), erect (+ sign) and virtual (behind the mirror at the same distance). Q14: f = R/2 = +15, u=−20. 1/v = 1/f − 1/u = 1/15 + 1/20 = 7/60 → v = +8.6 cm. m = −v/u = −8.6/−20 = +0.43 → h′ = 0.43×5 ≈ +2.15 cm. Image is virtual, erect, diminished, ~8.6 cm behind the mirror.

Q16: P = +2 D → f = 1/P = +0.5 m = +50 cm, a converging (convex) lens. Q17: P = −2 D → f = −50 cm, a diverging (concave) lens. (Q15: apply the mirror formula with the given data as in Q10-14.)

Concave mirror.

Slower.

Concave mirror (magnified erect image).

1/5 m = +20 cm (convex).

u=−30, f=−20. 1/v = 1/f − 1/u = −1/20 + 1/30 = (−3+2)/60 = −1/60 → v = −60 cm (real, in front).

u=−10, f=+15. 1/v = 1/15 − 1/10 = (2−3)/30 = −1/30 → v = −30 cm (virtual, erect, magnified — same side).

n = c/v → v = c/n = 3×10⁸ / 1.5 = 2×10⁸ m/s.

P = 2 + (−3) = −1 D (net diverging).

Image is real, inverted and twice the size of the object.

(1) Angle of incidence = angle of reflection. (2) The incident ray, the reflected ray and the normal all lie in the same plane.

Because of refraction — light bends as it passes from water to air, so the part in water appears displaced.

The point on the principal axis where rays parallel to the axis meet after reflection.

Beyond C → real, inverted, diminished. At C → real, inverted, same size. Between C and F → real, inverted, magnified. At F → image at infinity. Between P and F → virtual, erect, magnified.

A convex lens is thick in the middle, converges light, has positive focal length and forms real/virtual images (used as magnifier). A concave lens is thin in the middle, diverges light, has negative focal length and always forms a virtual, erect, diminished image.

All distances are measured from the pole. Distances measured in the direction of incident light are positive; opposite are negative. Heights above the principal axis are positive; below are negative. Hence concave mirror f is negative and convex mirror f is positive.