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An object is placed in front of convex lens of focal length (f =10 cm). The distance d for which image of the object will coincide with the object (irrespective of focal length of the mirror)

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Detailed Solution

$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$

$\frac{1}{10} = \frac{1}{v} - \frac{1}{- 15}$

$\frac{1}{v} = \frac{1}{10} - \frac{1}{- 15} = \frac{1}{30}$

v=-30 cm

If rays strike at pole of the mirror u = 0, V = 0

$∴$ for $2^{n d}$ refraction at lens object at pole of mirror gives image at the position of object

$∴ d = 30 c m$

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