A point source S is placed midway between two converging mirrors having equal focal length $f$ as shown in figure. For which value of $a$ only one image is formed?

\frac{f}{2}

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\frac{f}{3}

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2 f

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f

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Solution

The correct option is C $2 f$
Both the mirrors have equal focal length $f$ .
They will produce one image under two conditions.

Case I: When the source is at distance $2 f$ from each mirror i.e. the source is at centre of curvature of the mirrors, the image will be produced at the same point $S$ . So, $a = 2 f + 2 f = 4 f$ .

Case II: When the source $S$ is at distance $f$ from each mirror, the rays from the source after reflecting from one mirror will become parallel and so these parallel rays after the reflection from the other mirror fall on the object itself. So, only one image is formed.
Here, $a = f + f = 2 f$ .

Why this Question?

Note: Image formed will be at same position of object when light rays can retrace their path.

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A point source S is placed midway between two converging mirrors having equal focal length f as shown in figure. For which value of a only one image is formed?

A point source S is placed midway between two converging mirrors having equal focal length $f$ as shown in figure. For which value of $a$ only one image is formed?