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← JEE Main 2017 · 9 Apr · Shift 1
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JEE Main 2017 · 9 Apr · Shift 1, Physics question 22

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 and worked solution

Official answer: A

For the image to coincide with the object the rays must hit the mirror normally, i.e. the lens image must be at the mirror's centre of curvature. The lens gives 1v=115−120\frac1v=\frac1{15}-\frac1{20}, v=60v=60 cm, which is 55 cm behind the mirror. So R=55R=55 cm and f=27.5f=27.5 cm.