Question

Ten narrow slits are equally spaced 3.00 mm apart and illuminated with yellow light of wavelength 572 nm.

(a)

What are the angular positions (in degrees) of the second and fourth principal maxima? (Consider the central maximum to be the zeroth principal maximum.)

second principal maximum = .022°

fourth principal maximum = .044°

(b)

What is the separation (in m) of these maxima on a screen 2.0 m from the slits?

_____ m

Answer 1

Given, Wavelength, = 572 nm

The space between the slits = 3 mm

a)

for second maxima,

sin = (m / d)

sin = [2 x 572 x 10^-9 / 3 x 10^-3]

= sin^-1(3.813)

= 0.022 degree

for forth maxima,

= sin^-1(m / d)

= sin^-1[4 x 572 x 10^-9 / 3 x 10^-3]

= 0.044 degree

b)

For second principle maximum distance is,

y₂ = D*tan()

y₂ = 2 x tan(0.022)

= 7.68 * 10^-4 m

= 0.768 * 10^-3 m

For fourth principle maximum distance is,

y₄ = D*tan()

y₄ = 2 x tan(0.044)

y₄ = 1.535 * 10^-3 m

s = y₄ - y₂

= 1.535 * 10^-3 -  0.768 * 10^-3

= 0.767 * 10^-3 m