Question

The focal length of a concave mirror is f and the distance of the object from the principal focus is p.Then the ratio of the size of the image to the size of the object is given by:

Answer 1

I hope this answer help you

Answer 2

The correct answer to the question is $\ \frac{f}{p}$

CALCULATION:

The focal length of the concave mirror is given as f.

As per the sign convention for mirror, the focal length is taken as negative as it is measured opposite to the direction of light.

Hence, focal length f = -f.

The distance of the object from the principal focus is p.

Hence, the distance of object from the mirror [ u ] =  p+ f.

The object distance is also taken as negative as it is opposite to the direction of light.

Hence, u = - (p+f)

We are asked to calculate the ratio of size of image to the size of object.

The size of image to the size of object is known as the magnification [m]  of the mirror.

The relation between magnification,object distance and focal length is given as -                          

                              Magnification m = $\frac{f}{f-u}$

                                                          = $\frac{-f}{-f-[-(f+p)]}$

                                                          = $\frac{-f}{-f+f+p}$

                                                          = $\frac{-f}{p}$

Taking magnitude only, we get $m=\ \frac{f}{p}$         [ans]