1. (a) Iris (b) Retina (c) Ciliary Muscles. [Diagram:
Human Eye with these parts labeled].
2. Myopia: Image forms in front of retina. Correction:
Concave lens diverges rays to focus on retina.
[Diagram: Myopic Eye and Correction with Concave Lens]
3. Hypermetropia: Image forms behind retina. Correction:
Convex lens converges rays to focus on retina.
[Diagram: Hypermetropic Eye and Correction with Convex Lens]
4. Dispersion by Prism. Top: Red (Least deviated). Bottom:
Violet (Most deviated).
[Diagram: Dispersion showing VIBGYOR]
5. Two identical prisms placed inverted (Action and
Opposition). First disperses white light, second recombines it.
[Diagram: Newton's Recombination Experiment]
6. Sunlight enters water droplet $\to$ Refraction &
Dispersion $\to$ Total Internal Reflection $\to$ Refraction out $\to$ Rainbow.
[Diagram: Rainbow formation in water droplet]
7. [Diagram: Refraction through glass prism showing
$\angle i, \angle e, \angle D$]. $\angle i + \angle e = \angle A + \angle D$.
8. Due to atmospheric refraction, sun appears at horizon
when it is actually below it. Light bends from vacuum to atmosphere.
[Diagram: Advance Sunrise due to refraction]
9. Myopia: Focal length decreased (Lens too curved).
Hypermetropia: Focal length increased (Lens too flat).
[Diagram: Eye lens curvature comparison]
10. Light from stars bends towards normal as it travels
down through denser and denser layers of atmosphere. Eye projects ray straight back to a higher position.
[Diagram: Shift in star position]
11. Myopia (can't see far). Far point $x = 1.2$ m.
Using $f = -x$ for myopia correction: $f = -1.2$ m.
$P = 1/f = 1/(-1.2)$ $= -10/12 = -0.83$ D. Concave Lens.
12. Hypermetropia. Near point $N' = 1$ m = 100 cm. Normal
near point $N = 25$ cm.
Object at $u = -25$ cm should form virtual image at $v = -100$ cm.
$1/f = 1/(-100) - 1/(-25)$ $= -1/100 + 4/100 = 3/100$.
$P = 100/f(\text{cm}) = 3$ D. Convex Lens.
13. $P = -2.5$ D. $f = 1/P = 1/(-2.5) = -0.4$ m = -40
cm.
Negative power indicates Concave lens, so defect is Myopia.
14. (i) Distant: $P=-5.5$D. $f = 1/(-5.5) = -0.18$ m (-18
cm).
(ii) Near: $P=+1.5$D. $f = 1/1.5 = +0.67$ m (+67 cm).
15. Far point = 80 cm (0.8 m).
$f = -0.8$ m. $P = 1/(-0.8) = -1.25$ D. Nature: Concave Lens.
16. Same question as Q12. $P = +3.0$ D.
17. Person wants to read at $u=-25$ cm, but can only focus
at $v=-40$ cm.
$1/f = 1/(-40) - 1/(-25)$ $= -5/200 + 8/200$ $= 3/200$.
$f = 200/3$ cm = +66.67 cm. $P = 100/66.67 = +1.5$ D.
18. $n = c/v \implies v = c/n$.
$v = 3 \times 10^8 / 1.5 = 2 \times 10^8$ m/s.
19. Same as Q18. $v = 2 \times 10^8$ m/s.
20. Snell's Law: $n = \sin i / \sin r$.
$n = \sin 45^\circ / \sin 30^\circ$ $= (1/\sqrt{2}) / (1/2)$ $= 2/\sqrt{2} = \sqrt{2} = 1.414$.
21. ${}_w n_g = n_g / n_w = (3/2) / (4/3) = 9/8 = 1.125$.
22. Real, Inverted, Same Size means image is at $2F$. So
$v = 2f = 50$ cm.
So $f = 25$ cm = 0.25 m. Object also at $2F = 50$ cm.
$P = 1/0.25 = +4.0$ D.
23. Critical angle $\sin C = 1/n = 1/1.5 = 0.666$.
Given $\sin 42^\circ \approx 0.67$. So $C \approx 42^\circ$.
24. $P = P_1 + P_2 = +3.5 - 2.5 = +1.0$ D.
$f = 1/P = 1$ m = 100 cm.
25. $h_o = 5, f = +20, u = -30$. Lens Formula: $1/v - 1/u
= 1/f$.
$1/v = 1/20 + 1/(-30) = 3/60 - 2/60 = 1/60$. $v = +60$ cm (Real, behind lens).
$m = v/u = 60/(-30) = -2$. Image is Real, Inverted, Magnified ($10$ cm tall).
26. In space, there is no atmosphere. No particles to
scatter light. Scattering requires particles. Hence, no light enters eye from sky path $\to$ Dark.
27. At sunrise/set, light travels max distance through
atmosphere. Blue/shorter wavelengths scatter away completely. Only Red (longest $\lambda$) remains to reach
eye.
28. Stars are point sources; their light path changes due
to atmospheric turbulence (refraction), causing fluctuating intensity (twinkle). Planets are extended disks;
points average out.
29. Rayleigh Scattering. Air molecules scatter blue light
($I \propto 1/\lambda^4$) much more than red. This scattered blue light enters our eyes.
30. Red has longest wavelength. It is scattered the least
by fog/smoke/air. So it is visible from the longest distance.
31. Planets are closer and appear as extended sources
(collection of points). Variations in intensity from different points cancel each other out $\to$ No
twinkling.
32. At noon, sun is overhead, light travels least
distance. All colors scatter less, so they mix to appear white.
33. Near Point limit. Ciliary muscles cannot contract
enough to make the lens curved/thick enough to focus objects closer than 25 cm (Max power reached).
34. Image distance remains constant ($v \approx 2.3$ cm,
dist between lens and retina). Focal length changes to accommodate object distance.
35. (i) To increase horizontal field of view. (ii) For
stereoscopic vision (depth perception/3D).
36. No. Apparent position is slightly higher than true
position due to atmospheric refraction bending light towards the normal.
37. Rainbow requires water droplets in atmosphere to act
as prisms (dispersion+TIR). Rainfall provides these droplets.
38. Red light scatters least and penetrates fog/mist best
(Long wavelength).
39. Yes. Blue is scattered in all directions by
observation path.
40. Clouds contain large water droplets (larger than
$\lambda$ of light). Large particles scatter all wavelengths equally (Mie scattering) $\to$ White.
41. Defect: Myopia (Near-sightedness). Cannot see
distant objects (blackboard at 3m).
42. Correction: Concave Lens (Diverging Lens) of
appropriate power.
43. [Diagram: Myopic correction with concave lens].
44. Bending: Violet bends most, Red bends least.
45. Cause: Different colors travel with different
speeds in glass ($Speed \propto \text{Wavelength}$). Refractive index is different for each color.
46. Phenomenon: Rainbow.
47. Power is negative (-1.0 D), so lens is Concave. Defect
is Myopia. He can see near objects clearly (so reading is fine), but distant objects are blurry without
glasses.
48. Lens hardens with age (Presbyopia), loses
accommodation. Can't focus near (needs Convex for reading). If also myopic for distance, needs Concave.
Resolution: Bifocal Lenses (Upper: Concave, Lower: Convex).
49. Yellow light has longer wavelength than blue/violet,
so it scatters less in fog, providing better contrast and visibility.
50. Fine smoke particles are small enough to cause
Rayleigh scattering, scattering blue light more than red.
