In an experiment a convex lens of focal length 15 cm is placed… | JEE Main 2017 (9 Apr, Shift 1)

Q66JEE Main 2017 · 9 APR · SHIFT 1Medium

Combination of Lenses

In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is:

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Answer: (a)

Lens: $\frac{1}{v} = \frac{1}{15} - \frac{1}{20} = \frac{1}{60} \Rightarrow v = 60\text{ cm}$ behind the lens.
For the light to retrace its path, rays must hit the convex mirror normally, i.e. head towards its centre of curvature.
So $R = 60 - 5 = 55\text{ cm}$ and $f = \frac{R}{2} = 27.5\text{ cm}$ .
So the answer is (a) 27.5 cm.

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