Subject: Applied Physics 2

Topic: Interference And Diffraction

Difficulty: Medium

(a+b) = $\frac{2.54}{15000}$, wavelength λ$_1$ = 4000 AU

$ (a+b) sinθ = n λ_1 \\[2ex] sinθ= \frac{n λ_1}{(a+b)} \\[2ex] θ= sin^{-1} (\frac{n λ_1}{a+b}) \\[2ex] θ= sin^{-1} (\frac{n \times 4000 \times 10^{-8}}{2.54/15000}) \\[2ex] θ= 0.236 \times n \\[2ex] $

Substitute value of n as 1,2,3

Angles will be 13°, 28° , 45° …………………………(1)

For wavelength λ$_2$ = 7000 AU

$ (a+b) sinθ = n λ_2 \\[2ex] sinθ= \frac{n λ_2}{(a+b)} \\[2ex] θ= sin^{-1} (\frac{n λ_2}{a+b}) \\[2ex] θ= sin^{-1}⁡ (\frac{n \times 7000 \times 10^{-8}}{2.54/15000}) \\[2ex] θ= 0.413 \times n $

Substitute value of n as 1,2,3

Angles will be 24°, 56° …………………………….(2)

From equation 1 and 2 it is clear that first order spectrum is isolated whereas second and third order overlaps.