Question

Sunita takes a mirror which is depressed at the center and mounts it on a mirror stand. An enlarged image of her face is formed. She places the mirror on a stand along a meter scale at $ 15cm $ mark. In front of this mirror, she mounts a white screen and moves it back and forth along the meter scale till a sharp, well defined inverted image, often a distant tree, is formed on the screen at $ 35cm $ mark.
1. Name the mirror and find its focal length.
2. Why does Sunita get a sharp image up the distant building at $ 35cm $ mark?

Answer 1

Hint: It is told that the mirror is depressed at the center, hence it has to be a concave mirror. The difference between a concave mirror and convex mirror is the key to this answer. It can also be confirmed as a concave mirror as it forms an erect and enlarged image of Sunita ‘s face.

Complete answer:
 $ {1^{st}} $ part: From the characteristics of concave mirror, we know and only a concave mirror produces a virtual and erect image, when we place the object between the Pole and the focus (Sunita sees her face placing the mirror close to her face).
 $ {2^{nd}} $ part: Now let’s imagine the scenario, it is said that she places the mirror on a $ 15cm $ mark, then places a white screen to reflect the image and then finally settles at the $ 35cm $ mark, where she gets a sharp, well defined inverted image of the object.
Thus, it can say that the image of an object at infinity is produced when the mirror is at 35cm mark, hence it is its focal length, but see that the mirror was placed at $ 15cm $ earlier and now at $ 35cm $ , thus its focal length is $ = \left( {35 - 15} \right)\,cm = 20\,cm $ . (As a concave mirror forms an image at focus when the object is at infinity).
As the $ 35cm $ mark is the focal length of the mirror, Sunita gets a sharp image of the object.

Note:
For solving questions of mirrors, the characteristics of the mirrors are to be remembered. Also the difference between a lens and a mirror should be understood. We must know all the conditions for both the convex mirror and concave mirror so that we are able to find which mirror is used, what is its focal length and where the object is placed. Focal length is the distance of focus (the point at which all the parallel incident rays of light converge after reflecting a mirror) from the pole of a circular mirror.