Question

In a double-slit arrangement the slits are separated by a distance equal to 100 times the wavelength of the light passing through the slits.

(a) What is the angular separation in radians between the central maximum and an adjacent maximum?
(b) What is the distance between these maxima on a screen from the slits? •15.

Answer 1

(a) the angular separation is 0.01 rad

(b) distance between these maxima is 0.50 cm

Step-by-step explanation:

(a) The conditions for maximum in Young's experiment is:

d sin(θ) = m λ

where m = 0, 1 , 2 ...

The angle between the central maximum and it's adjacent can be determined by setting m equal to one. Therefore,

d sin(θ) = λ

θ = sin⁻¹(λ / d)

but d = 100 λ

Thus,

θ = sin⁻¹(λ / 100 λ)

θ = sin⁻¹(1 / 100)

θ = 0.01 rad

(b) The distance between the central axis and the first maximum is given by:

y = L sin(θ)

where

L is the distance between the slits and the screen.

Thus,

y = (50 cm) sin(0.01 rad)

y = 0.50 cm