A point source of light 'S' at a distance d from the screen A produces light intensity $I_{0}$ at the centre of the screen. If a completely reflecting mirror M is placed at a distance d behind the source as shown in the figure, treating object and its image as incoherent with each other, find the intensity at the centre of the screen.

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\frac{10}{9} I_{0}

\frac{8}{9} I_{0}

\frac{9}{8} I_{0}

\frac{9}{16} I_{0}

answer is B.

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Detailed Solution

Intensity $I = \frac{k}{r^{2}}$

Intensity at the screen without mirror

$I_{1} = \frac{k}{d^{2}}$

Intensity at the screen with mirror

Question Image

$I_{2} = \frac{k}{d^{2}} + \frac{k}{{(3 d)}^{2}}$

$= \frac{10}{9} \frac{k}{d^{2}}$

$= \frac{10}{9} I_{0}$

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