Maharashtra State Board · Class 12 · Physics · Chapter 7

Wave Optics — Formula Sheet

Board Formulas

12 formulas

1.Huygens' Principle★
$Every point on a wavefront is a source of secondary wavelets. New wavefront = envelope.$
Basis for laws of reflection and refraction. Wavelets propagate at wave speed.
2.Path Difference for Interference
$Δ x = d sin θ \approx \frac{d y}{D}$
y = distance of fringe from central maximum. D ≫ d assumed.
3.Conditions for Bright and Dark Fringes★
$Δ x = nλ (bright), Δ x = (n + \frac{1}{2}) λ (dark)$
n = 0, ±1, ±2, ... Central maximum at n = 0.
4.Fringe Width★
$β = \frac{λ D}{d}$
Uniform separation between consecutive bright (or dark) fringes.
5.Intensity in Two-Source Interference
$I = I_{1} + I_{2} + 2 I_{1} I_{2} cos ϕ$
φ = phase difference = (2π/λ)Δx. Maximum I_max = (√I₁+√I₂)².
6.Ratio of Max to Min Intensity
$\frac{I _{ma x}}{I _{min}} = (\frac{I _{1} + I _{2}}{I _{1} - I _{2}})^{2}$
Useful when amplitudes differ. Reduces to (a₁+a₂)²/(a₁−a₂)².
7.Single-Slit Diffraction Minima★
$a sin θ = nλ, n = \pm 1, \pm 2, \dots$
a = slit width. Central maximum has angular half-width sin⁻¹(λ/a).
8.Width of Central Diffraction Maximum
$W = \frac{2 λ D}{a}$
Twice the width of any secondary maximum. On a screen at distance D.
9.Malus's Law★
$I = I_{0} cos^{2} θ$
Intensity of light through two polarisers with axes at angle θ. Maharashtra specific 2-mark derivation.
10.Brewster's Law★
$tan i_{B} = n_{2} / n_{1}$
At Brewster's angle, reflected light is completely polarised perpendicular to plane of incidence.
11.Resolving Power of a Microscope
$RP = \frac{2 μ s i n θ}{λ}$
Higher μ (immersion oil) and larger θ → better resolution.
12.Resolving Power of a Telescope
$RP = \frac{D}{1.22 λ}$
Larger aperture D → better angular resolution.