Wave Optics Formula Sheet — Class 12 Physics

Optical Path: \(d' = nd\)
(\(d\): path in medium, \(n\): refractive index)
Resultant Intensity (Superposition): \(I = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos \phi\)
(\(\phi\): phase difference)
Relation between Phase and Path Difference: \(\phi = \frac{2\pi}{\lambda} \delta\)
(\(\delta\): path difference)
Young's Double Slit Maxima: \(y_n = \frac{n \lambda D}{d}\)
(\(y_n\): distance from center, \(D\): screen distance, \(d\): slit separation)
Fringe Width (Bandwidth): \(\beta = \frac{\lambda D}{d}\)
Thin Film Optical Path Difference: \(\delta = 2\mu d \cos r\) (for near normal incidence, \(\delta \approx 2\mu d\))
Single Slit Diffraction Minimum: \(a \sin \theta = n \lambda\)
(\(a\): slit width, \(n\): order of minimum)
Grating Equation (Maxima): \(\sin \theta = Nm\lambda\)
(\(N\): number of lines per unit length, \(m\): order of diffraction)
Fresnel Distance: \(z = \frac{a^2}{\lambda}\)
(\(a\): slit width)
Rayleigh's Criterion (Resolution): \(\theta = \frac{1.22 \lambda}{a}\)
(\(a\): aperture diameter)
Brewster's Law: \(n = \tan i_p\)
(\(i_p\): polarizing angle)
Malus's Law: \(I = I_0 \cos^2 \theta\)
(\(I_0\): initial intensity, \(\theta\): angle between polarizer and analyzer)

Wave Optics - Formula Sheet