Question

A double slit S₁ − S₂ is illuminated by a coherent light of wavelength \[\lambda.\] The slits are separated by a distance d. A plane mirror is placed in front of the double slit at a distance D₁ from it and a screen ∑ is placed behind the double slit at a distance D₂ from it (see the following figure). The screen ∑ receives only the light reflected by the mirror. Find the fringe-width of the interference pattern on the screen.

Answer 1

Given:-

Separation between the two slits = d

Wavelength of the coherent light =λ

Distance between the slit and mirror is D₁.

Distance between the slit and screen is D₂.

Therefore,

apparent distance of the screen from the slits,

\[D = 2 D_1 + D_2 \]

Fringe width, \[\beta = \frac{\lambda D}{d} = \frac{\left( 2 D_1 + D_2 \right) \lambda}{d}\]

Hence, the required fringe width is \[\frac{\left( 2 D_1 + D_2 \right)  \lambda}{d}.\]