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)

Solution

Physics sir · 4 steps

For the image to land back on the object, rays must hit the mirror head-on, so aim them at its centre.

1. Retrace condition. Light goes through the lens, reflects off the mirror and comes back through the lens to the object. That happens only if the rays strike the mirror normally, so they retrace their own path.
2. Where rays aim. Rays meet a spherical mirror normally only if they are heading towards its centre of curvature C. For the convex mirror, R = 2f = 30 cm, so C is 30 cm behind the mirror.
3. Lens image position. Without the mirror, the lens forms its real image exactly at that point C. Its distance from the lens is 8 + 30 = 38 cm.

   object to image = 12 + 8 + 30 = 50 cm

4. So. The real, inverted image is 38 cm beyond the lens and 12 cm more from the object, so it is 50 cm from the object.

The common slip: 38. Giving the image distance from the lens instead of from the object gives 38, not 50. Add the 12 cm between object and lens.

The idea to keep. Image falls back on the object only when rays hit a mirror normally, which means the lens image must sit at the mirror's centre of curvature, a distance 2f from the mirror.

Answer from the NTA final answer key. Solution by PrepWiser.