Coherent light of wavelength illuminates a double slit S₁ - S₂ . The separation between the slits is d . A plane mirror is positioned in front of the double slit at a distance D₁ , and a screen is located behind the double slit at a distance D₂ , as shown in the figure. The screen receives only the light reflected by the mirror. Determine the fringe-width of the interference pattern on the screen.

Step-by-step solution

The light from the double slits S₁ and S₂ travels a distance D₁ to reach the plane mirror. Upon reflection, the plane mirror forms virtual images of the slits, let's call them S₁' and S₂' . These virtual sources act as the coherent sources for the interference pattern on the screen. The virtual sources S₁' and S₂' are formed at a distance D₁ behind the mirror. The separation between these virtual sources remains the same as the original slits, so d' = d . The screen is located at a distance D₂ behind the plane of t