Question

In an experiment conducted using the Young's double-slit apparatus, the separation between the slits is 20 µm. A first-order constructive interference fringe appears at an angle of 2.5o from the zeroth order (central) fringe.
A. What wavelength of light is used in the experiment?
B. At what angle would the fourth-order (m = 4) bright fringe appear?
C. At what angle would the fourth-order (m=4) dark fringe appear?

Answer 1

To solve this problem, we use the formula
λ = s sin θ
where s is the separation and θ is the angle interference
So,
λ = 20 x 10^-6 sin 2.5
λ = 8.72 x 10^-7 m

The required angle for the fourth order bright fringe is
θb = sin⁻¹ (4λ / s) = sin⁻¹ (4 (8.72 x 10^-7 m)/ 20 x 10^-6 ) = 10.04°

The required angle for the fourth order dark fringe is
θd = sin⁻¹ (4.5 λ / s) = sin⁻¹ (4.5 (8.72 x 10^-7 m)/ 20 x 10^-6 ) = 11.31°