Question

What is the effect on the fringe width of interference fringes in a Young's double slit experiment due to each of the following operations.
(a) The screen is moved away from the plane of the slits.
(b) The (monochromatic) source is replaced by another (monochromatic) source of shorter wavelength.
(c) The separation between the two slits is increased
(d) The width of two slits are slightly increased
(In each operation, take all parameters, other than the one specified to remain unchanged)

Answer 1

Bandwidth;

$\beta =\left(\frac{D}{d}\right)\lambda$

where

D is Distance between screen to slits

d is Distance between the slits

$\lambda$ is wavelength

(a) Screen is moved away--Here,D increases

Hence, bandwidth increases

(b) Wavelength decreases --here, $\lambda$decreases

Hence, bandwidth decreases

Wavelength increases -- Here, $\lambda$ increases

Hence, bandwidth increases

(c) Slit width increase -- Here, d increases

Hence, bandwidth decreases

(d) As the source slit width increases, fringe pattern gets less and less sharp. When the source slit is so widethen the interference pattern disappears.