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 another side of the lens at $8$ cm as shown in the figure. The image of the 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
Numerical value type. Enter your answer.
Answer: 50
For the final image to coincide with the object, the rays must retrace their path, so they must strike the convex mirror normally. That happens when the lens alone would form its image at the mirror's centre of curvature, $R = 2f = 30$ cm behind the mirror.
Without the mirror, the image is therefore $8 + 30 = 38$ cm from the lens, on the far side.
Distance between object and image $= 12 + 38 = 50$ cm.
Solution by Sreeraj P, M.Sc Physics