Question

A point object is placed in the middle of two concave mirrors. The focal length of each mirror is 10 cm to obtain single image of point object, the distance between two mirrors in cm will be
A. 10 cm
B. 20 cm
C. 30 cm
D. 40 cm

Answer 1

Hint: Concave mirrors form both virtual and real images. Here two concave mirrors are used and images should be formed at one point only. There is a specific point where the image formed due to two mirrors will be at one point and we will discuss that case. Object position and image position will be the same here.

Complete answer:
Various positions of placing an object in front of a concave mirror gives us various positions of images.
If an object is placed between the pole and focus of the concave mirror then image will be formed on the other side of the mirror. That image formed can be enlarged or diminished and virtual.
Now if we place an object between focus and center then the image is formed away from the center and the image will be real and inverted. The size of the image will be bigger than an object as shown in the diagram.

If the object is placed exactly at center the image also will be formed exactly at the center just as shown in the diagram below.

P denotes the pole and F denotes the focus and C denotes the center.
Let us imagine if we place another concave mirror opposite to this and if we place an object at the mutual centers i.e at the midpoint of these mirrors then the image formed will be only one and formed exactly at the object.
Focal length of mirrors is 10cm so the center will be at twice the focal length distance from the pole that means 20cm.
So in order to satisfy all the required conditions the distance between concave mirrors must be 40cm such that the midpoint will be the center of two mirrors and we can place objects there.

Hence option D is correct.

Note:
It is to be noted that the distance between pole and center would be radius and equal to twice of the focal length in case of mirror. For the plane mirror focal length will be infinity.