Test: Mirror Formulae - UPSC

Consider a plane-mirror and a fixed incident ray of light reflecting from the surface at an angle θi. Before the mirror has rotated, the angle of incidence is θ as is the angle of reflection. If the mirror is rotated through an angle φ the normal is rotated by an angle &phi and thus the angle of incidence increases to θ+φ. Therefore, the angle of reflection must also increase by φ to θ+φ The difference between the final angle of reflection and the initial angle of reflection and is 2φ.
Hence, For a fixed incident ray, the angle of the reflection is twice the angle through which the mirror has rotated: thetaf= 2φ

u = -60 cm, v = -30 cm

m = – v/u = – (-60)/-30 = - 2

The correct option is B.

We know that, if the magnification value is negative sign in the concave mirror, then the image will be real and inverted. Especially, when you come to concave mirror, the images are formed at the left of the mirror. So, it forms real and inverted.

It can either be a convex mirror or concave mirror. It depends upon the position of the object. u is always negative so in order to get magnification positive v must be negative. If the object is kept between pole and the focus of the mirror, then it will form a virtual image behind the mirror and v will be +.

Magnification is the ratio of height of the image to the height of the object. If the image size is double of object size, then the magnification is equal to two.

The formula for the focal length of a mirror is 1/f = 1/v + 1/u , where f is the focal length, v is the image distance, and u is the object distance.

If we substitute the given values (remembering that for a convex mirror, the object distance is negative), we get:

1/f = 1/(-5.8cm) + 1/(-14cm)

Solving for f, we get f = -4.1 cm.

Hence, the correct answer is

2. 4.1cm.

Object is always kept on the left side of the mirror therefore its distance is always negative when taken from left of pole.

Magnification is thr ratio of size of image to size of object and since it is a ratio of tel similar quantities hence it is unitless. 

Correct option is A.

The image formed by a convex mirror is always smaller in size than the object; hence its magnification is less than 1.