An object is placed on the principal axis of convex lens of focal length 10cm as shown. A plane mirror is placed on the other side of lens at a distance of 20 cm. The image produced by the plane mirror is 5cm inside the mirror. The distance of the object from the lens is ___________ cm.

Solution

Physics sir · 4 steps

Work backwards from the mirror: its image tells you exactly where the lens put its image.

1. Mirror first. A plane mirror forms its image as far behind it as the object is in front. The image is 5 cm inside the mirror, so the mirror's object is 5 cm in front of it.
2. Locate lens image. The mirror's object is the image formed by the lens. It lies 20 - 5 = 15 cm from the lens, on the mirror side, so v = +15 cm. It is a real image.

   1/v - 1/u = 1/f ⇒ 1/15 - 1/u = 1/10

3. Solve for u. 1/u = 1/15 - 1/10 = (2 - 3)/30 = -1/30, so u = -30 cm. The minus sign means the object is on the side opposite the mirror, as in the figure.
4. So. The object is 30 cm from the lens.

The idea to keep. In lens-plus-mirror problems, the image from one element is the object for the next. Trace the light in order and use the plane mirror's equal-distance rule to fix positions.

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