Question

A five-slit system with 9.0 μm slit spacing is illuminated with 645 nm light.

Part A

Find the angular positions of the first two maxima.

Enter your answers numerically separated by a comma.

θ1,θ2 = .... degree

Part B

Find the angular positions of the third and sixth minima.

Enter your answers numerically separated by a comma.

φ3,φ6 =

∘

Answer 1

here d = 9um = 9 x 10^-6 m lemda = 645nm = 645 x 10^-9 m   

(a) for the m,axima

d sinQ = n(lemda)

for first maxima n = 1

so sinQ₁ = ( 1 x 645 x 10^-9 ) / ( 9 x 10^-6 )

= 0.0716

Q₁ = sin^-1(0.0716) = 0.0717^o   Ans

for second maxima n = 2

d sinQ₂ = 2 x 645 x 10^-9

sinQ₂ = 0.1433

Q₂ = sin^-1(0.1433) = 0.1438^o   Ans

(b) for the minima

d sinQ = ( n + 1/2 ) lemda

for third minima n = 3

sinQ₃ = ( 3 + 0.5 ) x ( 645 x 10^-9 ) / ( 9 x 10^-6 )

= 0.2508

Q₃ = sin^-1(0.2508) = 0.253^o   Ans

for the sixth minima n = 6

d sinQ₆ = 6.5 x 645 x 10^-9

sinQ₆ = 0.4658

Q₆ = sin^-1(0.4658) = 0.484^o   Ans