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In the optical arrangement shown, a point source S emits light of wavelength lambda that reaches the screen only after reflection. The source lies between two parallel mirrors, at a perpendicular distance d below the upper mirror and 3d above the lower mirror. A screen is placed at a large horizontal distance D, and point P on the screen is level with the upper mirror. For P to be the 2nd maximum, the wavelength lambda must be (given D >> d and d >> lambda)

1. 12d²/D
2. 6d²/D
3. 3d²/D
4. 24d²/D

Correct answer: 6d²/D

Solution

The two reflecting surfaces produce two virtual images of S. The image in the upper mirror is at distance d above it (so d above the upper surface), and the image in the lower mirror is at distance 3d below it. The separation between the two virtual sources is found from their geometry, and the resulting two-source interference at P (with the extra pi phase shift on reflection) sets the bright-fringe condition. Working through the geometry gives the 2nd maximum condition lambda = 6d²/D.

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