Ray Optics
1. Introduction
Ray optics treats light as rays that travel in straight lines. It explains reflection, refraction, image formation, and the working of optical instruments.
2. Reflection
2.1 Laws of Reflection
- Incident ray, reflected ray, and normal lie in the same plane.
- Angle of incidence = angle of reflection (i = r).
2.2 Spherical Mirrors
Mirror formula: 1/f = 1/v + 1/u (sign convention: all distances from pole). Magnification: m = -v/u.
| Mirror | Focal length | Uses |
|---|---|---|
| Concave | f = R/2 (negative) | Shaving mirror, telescope |
| Convex | f = R/2 (positive) | Rear view mirror |
3. Refraction
3.1 Snell's Law
n₁ sin i = n₂ sin r, where n is the refractive index.
3.2 Refractive Index
n = c/v (absolute), n₂₁ = n₂/n₁ (relative).
3.3 Critical Angle and Total Internal Reflection
sin i_c = n₂/n₁ (for n₁ > n₂). When i > i_c, light is entirely reflected back.
'Total internal reflection is used in optical fibres, mirages, and diamond cutting.'
4. Lenses
4.1 Lens Maker's Formula
1/f = (n₂₁ - 1)(1/R₁ - 1/R₂)
4.2 Lens Formula
1/f = 1/v - 1/u (sign convention as per Cartesian system).
4.3 Power of a Lens
P = 1/f (in metres). Unit: dioptre (D).
4.4 Magnification
m = v/u. For combinations: m = m₁ × m₂.
4.5 Combination of Lenses
1/F = 1/f₁ + 1/f₂. P = P₁ + P₂.
5. Prism
5.1 Angle of Deviation
δ = i + e - A, where A is the prism angle.
5.2 Minimum Deviation
At minimum deviation: i = e, δ = δ_m. n = sin((A + δ_m)/2)/sin(A/2).
6. Optical Instruments
6.1 Microscope
Simple microscope: M = 1 + D/f (at near point), M = D/f (at infinity).
Compound microscope: M = (L/f₀)(1 + D/f_e), where L is tube length.
6.2 Telescope
Astronomical telescope (normal adjustment): M = f₀/f_e. Length = f₀ + f_e.
Cassegrain telescope: Uses concave primary and convex secondary mirror.
7. Worked Problems
Problem 1: A concave mirror of focal length 20 cm forms an image at 30 cm from the mirror. Find object distance. Solution: 1/f = 1/v + 1/u ⇒ 1/(-20) = 1/(-30) + 1/u (f negative for concave, v negative for real image). 1/u = -1/20 + 1/30 = (-3+2)/60 = -1/60. So u = -60 cm.
Problem 2: A lens of power +5D is placed in contact with a lens of power -3D. Find the power and focal length of the combination. Solution: P = P₁ + P₂ = 5 + (-3) = 2 D. f = 1/P = 1/2 = 0.5 m = 50 cm.
Problem 3: A prism of angle 60° gives minimum deviation of 40°. Find refractive index. Solution: n = sin((A + δ_m)/2)/sin(A/2) = sin(50°)/sin(30°) = 0.766/0.5 = 1.532.
8. Common Mistakes
'Students must use consistent sign conventions. The Cartesian sign convention (distances measured from the pole/optical centre) is recommended for all calculations.'
9. ISC Exam Focus
| Topic | Theory Marks | Practical Marks |
|---|---|---|
| Mirrors | 3 | 2 |
| Refraction | 3 | 2 |
| Lenses | 4 | 3 |
| Prism | 3 | 2 |
| Optical instruments | 4 | 2 |
10. Self-Test Questions
- Derive the mirror formula for a concave mirror.
- A convex lens of focal length 15 cm forms an image at 20 cm from the lens. Find object distance and magnification.
- Derive the lens maker's formula.
- Explain total internal reflection with two everyday examples.
- An astronomical telescope has an objective of focal length 100 cm and eyepiece of 5 cm. Find its magnifying power and length.
