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JEE Main · 2021 · 26 Aug 2021 · Shift 2 · Geometrical Optics

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An object is placed at a distance of 12 cm from a convex lens. A convex mirror of focal length 15 cm is placed on other side of lens at 8 cm as shown in the figure. Image of object coincides with the object. When the convex mirror is removed, a real and inverted image is formed at a position. The distance of the image from the object will be _____ (cm).

Answer: 50

Solution

The final image falls back on the object only if the rays meet the convex mirror along its normals and retrace their path. Rays directed towards the centre of curvature of a convex mirror strike it normally, so the lens on its own must converge the light to that centre, a distance cm behind the mirror.
The mirror stands cm beyond the lens, so this image point lies

to the right of the lens. Removing the mirror leaves the lens forming exactly this real inverted image, and the object is cm to the left of the lens, so the image is

from the object.

JEE Main · 2021 · 26 Aug 2021 · Shift 2 · Integer answer

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