Question

A thin convex lens of focal length 6cm is placed 4cm left of a thin concave lens of focal length 6 cm. A point size object is placed at 24 cm from convex lens. The final image is formed at what distance ?
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Answer 1

The final image, formed by the combination, is coinciding with the object itself. This implies that the rays, from the object, are retracing their path, after refraction from the lens and reflection from the mirror. The (refracted) rays are, therefore, falling normally on the mirror. Thus the image of the convex lens should form at the center of curvature of the convex mirror.We first find the image distance of the convex lens using the lens formula..

$\frac{1}{v} - \frac{1}{( - 12)} = \frac{1}{10}$

$\frac{1}{v} = \frac{1}{(10)} - \frac{1}{12} = \frac{2}{120}$

v = 60cm ( this is at the centre of curvature of the mirror )

Thus we get the radius of curvature as

v - d = R

60 - 10 = R

=> R = 50cm

Thus we get the focal length as

F = R/2 = 50/2 = 25cm