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 (figure 17-E2). The screen ∑ receives only the light reflected by the mirror. Find the fringe-width of the interference pattern on the screen.

Figure

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,
$$\begin{gathered} D=2D_1+D_2 \\ \mathrm{Fringe}\mathrm{width},\beta =\frac{\lambda D}{d}=\frac{\left(2D_1+D_2\right)\lambda }{d} \end{gathered}$$

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