Ray Optics and Wave Optics (Class 12)
Why This Chapter Matters
Optics gives 10-14 marks in Class 12 boards — one of the highest sections. Mirrors, lenses, total internal reflection, interference (Young's double slit), and diffraction are all tested.
Core Concepts
1. Reflection (Mirrors)
Mirror formula: 1/v + 1/u = 1/f. f = R/2.
Magnification: m = -v/u = hᵢ/h₀.
Sign convention: Object always left of mirror. Distances measured from pole. Left = negative, right = positive. Above axis = positive, below = negative.
Concave: f negative. Convex: f positive.
2. Refraction (Snell's Law)
n₁ sinθ₁ = n₂ sinθ₂. n = c/v = speed of light in vacuum/speed in medium.
n = real depth/apparent depth.
Total Internal Reflection (TIR):
Occurs when light goes from denser to rarer medium at angle > critical angle.
sin θ_c = n₂/n₁ (n₁ > n₂).
Applications: Optical fibres, diamond sparkle, mirages.
3. Lenses
Lens formula: 1/v - 1/u = 1/f.
Power: P = 1/f (metres). Unit: Dioptre (D). Convex lens: +ve power.
Lensmaker's equation: 1/f = (n-1)[1/R₁ - 1/R₂].
Combination: 1/f = 1/f₁ + 1/f₂. P = P₁ + P₂.
Refraction at spherical surface: n₂/v - n₁/u = (n₂-n₁)/R.
4. Prism
Refraction through prism: n = sin((A+D)/2)/sin(A/2).
A = prism angle, D = angle of deviation (minimum at D_min).
Dispersion: different colours refract differently. Violet bends most, Red least.
Angle of deviation δ = (n-1)A for thin prism.
5. Wave Optics — Young's Double Slit Experiment
Interference of light. Fringe width β = λD/d.
λ = wavelength, D = distance to screen, d = slit separation.
Bright fringe: path difference = nλ (n = 0, ±1, ±2...).
Dark fringe: path difference = (2n-1)λ/2.
At centre (n=0): always bright.
Intensity: I = 4I₀cos²(δ/2) where δ = phase difference = 2π/λ × path difference.
I_max = 4I₀ (at constructive). I_min = 0 (at destructive, for equal intensities).
6. Diffraction
Bending of light around edges of obstacles.
Single slit (width a): first minimum at sinθ = λ/a.
Resolving power: ability to distinguish two closely spaced objects.
Rayleigh's criterion: θ_min = 1.22λ/D (D = aperture diameter).
Board Examples
Q1: Find image position and magnification for object 20cm from concave mirror (f=15cm).
1/v + 1/u = 1/f → 1/v + 1/(-20) = 1/(-15) → 1/v = -1/15 + 1/20 = (-4+3)/60 = -1/60.
v = -60 cm (real, same side as object). m = -v/u = -(-60)/(-20) = -3 (inverted, magnified 3×).
Q2: In YDSE, λ=600nm, slit separation 0.6mm, screen at 1.5m. Find fringe width.
β = λD/d = 600×10⁻⁹ × 1.5 / 0.6×10⁻³ = 1.5×10⁻³ m = 1.5 mm.
PYQs (CBSE)
CBSE 2023: Draw a ray diagram showing total internal reflection in an optical fibre. What is the condition for TIR?
Condition: (1) Light must travel from denser to rarer medium. (2) Angle of incidence must be greater than critical angle.
[Diagram: light bouncing along fibre with TIR at core-cladding interface]
CBSE 2022: A biconvex lens has radii of curvature 20cm each. n=1.5. Find focal length.
1/f = (1.5-1)(1/20-1/(-20)) = 0.5×(1/20+1/20) = 0.5×1/10 = 1/20. f = 20cm.