Question

A concave mirror forms an image of the sun at a distance of $12cm$ from it. Then:
A. The radius of curvature of this mirror is $6cm$
B. To use it as a shaving mirror, it can be held at a distance of $8 - 10cm$ from the face.
C. If an object is kept at a distance of $24cm$ from it, the image formed will be of the same size as the object
D. All the above alternatives are correct

Answer 1

Hint - To solve this problem, firstly we will learn about mirrors specially the concave mirrors including its uses, focal length of the mirror and the concept behind them. We will be gathering as much information about these mirrors and hence by using this information we can easily approach our answer.

Complete step-by-step answer:
Mirror - Narrow beam of light that incident on its surface bounces in a single direction. This characteristic of a mirror is called reflection, differentiating a mirror from objects that scatter light in many directions.
Concave mirror is reflecting surface bulging inward. It is converging in nature; it takes light from various sources and then converges it in one direction and the image form may be real or virtual depending on the position of the object. Image forms may be diminished, same sized or magnified, the examples of concave mirrors are mirrors used in Automobile headlight, reflecting telescopes, torch light etc.
Focal length is used to calculate how strongly the system converges or diverges light. A positive focal length indicates that a system converges light, while negative focal length indicates that the system diverges light.
Concave mirror is forming an image of the sun at a distance of $12cm$ (Given in the question)
So, the focal length of mirror is $12cm$
Radius of mirror if $f \times 2 = 24cm$
For shaving we need a virtual image which should be magnified and erect.
So, the mirror must be kept at a reasonable distance of $8 - 10cm$ which is within focus and pole.
As the radius is $24cm$ the object placed at the center forms an image at the same place.

Hence, both option B and C are the correct answer –
The radius of curvature of this mirror is $6cm$
To use it as a shaving mirror, it can be held at a distance of $8 - 10cm$ from the face.

Note - A concave mirror is also called a converging mirror which has its reflecting surface bulging inward. The concave mirror is used in Automobile headlight, shaving mirror, ophthalmoscope, Astronomical telescopes, reflecting telescopes etc. They are mainly used for providing a magnified image of the face for applying make-up or shaving.