1. Laws of Reflection: (i) The incident ray, the
reflected ray, and the normal to the reflecting surface at the point of incidence, all lie in the same
plane. (ii) The angle of incidence is equal to the angle of reflection ($\angle i = \angle r$).
2. Angle with mirror surface = 30°. Therefore, Angle of
Incidence $i = 90^\circ - 30^\circ = 60^\circ$. By laws of reflection, Angle of Reflection $r = i =
60^\circ$.
3. Lateral Inversion: The phenomenon where the left
side of an object appears as the right side of the image in a plane mirror. Example: 'AMBULANCE' written
backwards.
4. Object distance $u = 2$ m. Image distance in plane
mirror = Object distance = 2 m. Total distance = $2 + 2 = 4$ m.
5. Minimum size of plane mirror required = $H/2$ (Half the
height of the person).
6. Principal Focus (Concave): Point on principal
axis where parallel rays converge after reflection.
7. Ray retraces its path. A ray passing through Center of
Curvature falls normally ($\angle i = 0$) on the mirror, so it reflects back along same line ($\angle r =
0$).
8. $R = 2f$.
9. $R = +30$ cm. $f = R/2 = +15$ cm.
10. Virtual, Erect, and Diminished.
11. Object at C: Image at C. Real, Inverted, Same Size.
[Generate Image: Ray diagram for Concave Mirror. Object at C. Real, Inverted Image at C. Same size.]
12. Object between P and F: Image behind mirror, Virtual,
Erect, Magnified.
[Generate Image: Ray diagram for Concave Mirror. Object between P and F. Virtual, Erect, Magnified Image
behind mirror.]
13. Between C and F. Image forms beyond C.
14. To produce a magnified, erect image of the tooth
(Object placed within focus).
15. Image at Focus (F). Real, Inverted, Highly Diminished
(Point-sized).
[Generate Image: Ray diagram for Concave Mirror. Parallel rays from Infinity converging at Focus (F).]
16. $h=5, u=-20, f=-15$ (Concave).
$1/v = 1/f - 1/u$ $= 1/(-15) - 1/(-20)$ $= -4/60 + 3/60$ $= -1/60$.
$v = -60$ cm. Real, Inverted, Magnified ($m = -v/u$ $= -(-60)/-20$ $= -3$). Size = 15 cm.
17. Convex: $R=+3, f=+1.5, u=-5$.
$1/v = 1/1.5 - 1/(-5)$ $= 10/15 + 3/15$ $= 13/15$.
$v \approx 1.15$ m (Behind mirror). Virtual, Erect.
18. $u=-10$. Real image means same side ($v=-20$).
$1/f = 1/(-20) + 1/(-10)$ $= -3/20$. $f = -6.67$ cm. Concave Mirror.
19. Real means Inverted. $m = -3$.
20. Diverging (Convex): $f=+20, u=-25$.
$1/v = 1/20 + 1/25$ $= 9/100$. $v = +11.1$ cm. Virtual, Erect.
21. $n_m = c/v$.
22. $v = c/n$ $= 3 \times 10^8 / 1.5$ $= 2 \times 10^8$
m/s.
23. Speed in diamond is much less ($1/2.42$ times $c$).
Optically dense.
24. Ray bends towards normal (Air to Glass), then away
from normal (Glass to Air). Emergent ray parallel to incident ray.
[Diagram: Rectangular Glass Slab Refraction]
25. Ratio of sine of angle of incidence to sine of angle
of refraction is constant. $\frac{\sin i}{\sin r} = n$.
26. Convex: Converging, Thicker at center. Concave:
Diverging, Thinner at center.
27. Object at $2F_1 \to$ Image at $2F_2$. Real, Inverted,
Same Size.
[Generate Image: Ray diagram for Convex Lens. Object at 2F1. Real, Inverted Image formed at 2F2. Same
size.]
28. Object between O and $F_1 \to$ Virtual, Erect,
Magnified.
[Generate Image: Ray diagram for Convex Lens. Object between F1 and Optical Center. Virtual, Erect,
Magnified Image on same side.]
29. At $2F_1$.
30. Concave lens always forms Virtual, Erect, Diminished
image between O and F.
[Generate Image: Ray diagram for Concave Lens. Object anywhere. Virtual, Erect, Diminished Image between
F and O.]
31. $f=+10, v=+12$ (Real).
$1/u = 1/v - 1/f$ $= 1/12 - 1/10$ $= -1/60$. $u = -60$ cm.
32. $u=-25, f=+10$.
$1/v = 1/10 - 1/25$ $= 3/50$. $v = +16.67$ cm. Real, Inverted.
33. Concave: $f=-15, v=-10$ (Virtual).
$1/u = 1/(-10) - 1/(-15)$ $= -1/30$. $u = -30$ cm.
34. $P=-2.0$ D. $f = 1/P = -0.5$ m = -50 cm. Concave Lens.
35. $P=+1.5$ D. $f = 1/1.5 = +0.67$ m. Convex
(Converging).
36. Power of a lens with focal length 1 meter.
37. $P = +2 - 0.5 = +1.5$ D.
38. $f = 1/1.5 = 0.67$ m.
39. To increase magnification, sharpness, and reduce
aberrations.
40. $P = P_1 + P_2 + P_3$.
41. $n_w = 4/3, n_g = 3/2$.
Refractive index of glass w.r.t water ${}_w n_g = n_g / n_w$ $= (3/2) / (4/3)$ $= 9/8$ $= 1.125$.
42. $P = -0.5$ D.
$f = 1/P = 1/(-0.5) = -2$ m. Nature: Concave Lens (Diverging).
43. $v = 2 \times 10^8$ m/s, $c = 3 \times 10^8$ m/s.
$n = c/v = 3/2 = 1.5$.
44. $P_1 = +3.5$ D, $P_2 = -2.5$ D.
Net Power $P = +3.5 - 2.5 = +1.0$ D.
Focal length $f = 1/P = 1/1 = +1$ m (+100 cm). Converging.
45. Unit of Refractive Index: It is a ratio of similar
quantities (speeds), so it has No Unit.
46. (i) Normal incidence ($i=0$). (ii) $n_1 = n_2$.
47. No. Real objects always produce virtual images in
convex mirrors.
48. Because it converges parallel rays to a focus.
49. Behave like prisms with bases towards principal axis.
50. Focal length increases (Power decreases).
51. $v = 3 \times 10^8 / 1.5$ $= 2 \times 10^8$ m/s.
52. $v = 3 \times 10^8 / (4/3)$ $= 2.25 \times 10^8$ m/s.
53. $n = 3/2 = 1.5$.
54. $v = 3 / 2.42$ $\approx 1.24 \times 10^8$ m/s.
55. $n_{AB} = v_B/v_A = 2.5/2 = 1.25$.
