Question

Determine the type of mirror of used, if the magnification value is $+{\displaystyle \frac{1}{3}}$
(A) Concave Mirror
(B) Convex Mirror
(C) Plane Mirror
(D) Plano convex mirror

Answer 1

Hint The convex mirror always produces images of smaller size than the size of object. So, the value of magnification is always less than 1. For the concave mirror, the value of magnification is greater than 1. In the plane mirror, the magnification value is equal to 1.

Complete step-by-step answer:
The process of increasing the size of an image as compared to the size of an object is called Magnification. We can also say that it is the ratio of the distance of an image to the distance of an object. It is denoted by $M.$
Here, $v$ is the distance of image and $u$ is the distance of the object.
$M={\displaystyle \frac{v}{u}}$
The height of an object is always taken as positive as it is above the principal axis. The sign of image may vary according to the type of formation of image. The height of formed images which are real are assigned a negative sign while the height of virtual images are assigned a positive sign.
When the value of magnification positive and negative both, then the mirror is said to be concave because the images can be real and virtual both therefore, according to sign convention magnification can be assigned positive and negative sign.
When the value of magnification is between 0 and 1, then the mirror is said to be a convex mirror.
If the magnification is +1, then the mirror is called a plane mirror.
According to question, the value of magnification is $+{\displaystyle \frac{1}{3}}$ which is equal to $+0.3$
According to the above statements, we can conclude that the value of magnification is between 0 and 1 and it is the positive value. Therefore, the mirror is a convex mirror.

Hence, option (B) is correct.

Note The value of convex mirror is always taken as positive because it produces an erect image of the object. Therefore, according to sign convention it is always assigned a positive sign.
Magnification value of a plane mirror is always $+1$ because the height of the image is always equal to the height of the object and this mirror always produces an erect image.