Question

An object is placed at a distance of $ 2f $ from a concave mirror. Light reflected from the mirror falls on a plane mirror. The distance of the plane mirror from the concave mirror equals $ f $ .The distance of the final image from the concave mirror (due to reflection at both concave and plane mirror) is:
A. $ f $
B. $ \dfrac{f}{2} $
C. $ 2f $
D. Zero

Answer 1

Hint: To solve this problem we will be first learning about Concave mirror, concept behind them and applications. And then by using the Mirror formula we will be easily approaching our answer.

Complete step-by-step answer:
Concave mirror: A concave mirror which is also called converging mirror, having a reflected surface bulging inward. They are used to focus light.
Concave mirrors are used for producing both real and virtual images. They can be upright or inverted.
Mirror formula: Mirror formula is defined as the equation related object distance and image distance with focal length is known as a mirror equation. It is also referred to as the mirror formula.
Focal length: The focal length of an optical system is an estimate how strongly it converges or diverges light. A $ + $ focal length indicates that a system converges light, while a $ - $ focal length indicates that the system diverges light.
Now,
For a concave mirror, when the object is at $ 2f $ .image is formed at $ 2f $ .
Hence, $ {v_1} = - 2f $ for concave mirror
Image formed by concave mirror sets as an object to plane mirror.
Position of plane mirror concerning concave mirror is $ d = - f $
So, position of object for plane mirror is $ {v_2} = - f. $ (origin shifted to left)
Therefore, position of image for plane mirror is $ {v_2} = + f $
Position of final image, the concave mirror is $ {v_3} = {v_2} + d = 0 $ (origin shifted to right)
The right answer is option D. Zero (0)

Note - Concave mirror reflects light inward to the one focal light. They are mostly used to focus light. A concave mirror usually shows different images types depending on the distance between the mirror and the object. Concave mirror is used in shaving mirror, used in ophthalmoscope, used in astronomical telescopes, used in headlight.