Shortcut Methods

Shortcut Methods and Tricks to Solve Numerical Problems on Interference of Light

Double-Slit Interference

Fringe width: $β = \frac{λ D}{d},$ where (\beta) is the fringe width, (\lambda) is the wavelength of light, (D) is the distance from the slits to the screen, and (d) is the slit separation.
Separation of bright fringes: $Δ x = \frac{λ D}{d}$
Intensity distribution: $I = I_{0} \cos^{2} (\frac{π d}{λ D} x),$ where (I_0) is the maximum intensity and (x) is the distance from the central fringe.

Michelson Interferometer

Wavelength of light $λ = \frac{2 D}{N},$ where (D) is the path difference and (N) is the number of fringes observed.
Coherence Length $l_{c} = \frac{λ}{2 (Δ λ)},$ where (l_c) is the coherence length and (\Delta \lambda) is the spectral bandwidth of the light source.

Young’s Double-Slit Experiment

Fringe spacing $x = \frac{λ D}{d},$ where (x) is the fringe spacing, (\lambda) is the wavelength of light, (D) is the distance to the screen, and (d) is the slit separation.
Fringe width $β = \frac{2 λ D}{d},$ where (\beta) is the fringe width.
Total Number of fringes: $N = \frac{D}{β} = \frac{d}{2 λ}$

Coherence and Incoherence

Coherent sources: Emit waves with the same frequency, constant phase difference, and a definite phase relation.
Incoherent sources: Emit waves with random phase differences and no definite phase relation.

Thin Film Interference

Condition for constructive interference: $2 t n = m λ, m = 0, 1, 2, 3, \dots$
Condition for destructive interference: $2 t n = (m + \frac{1}{2}) λ, m = 0, 1, 2, 3, \dots$ where (t) is the film thickness, (n) is the refractive index of the film, (\lambda) is the wavelength of light, and (m) is the order of interference.

Shortcut Methods

Shortcut Methods

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