Question

When an object is at a distance x1 and x2 from the poles of a concave mirror, images of same magnification are formed. The magnitude of focal length of the mirror is ?
a) (x1 +x2)/2
b) (x1 - x2)/2
C) x1 + x2
D) x1 - x2

Answer 1

C) x1 + x2 The magnitude of focal length of the mirror is

Answer 2

So, that the focal length’s magnitude of the mirror is  x_{1}+x_{2} (option C).

Solution:

The image formed will be the same from both the objects $x_{1} and\ x_{2}$ so taking into consideration the first object.

Using mirror formula for $x_{1}$

$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$ Where f is the focal length and v is the distance of image.

So we have,

$\frac{1}{f}=\frac{1}{v}-\frac{1}{x_{1}}$

From here, the distance of image is  

$v=\frac{f x_{1}}{x_{1}+f}$

Using this distance of image in second object

$\frac{1}{f}=\frac{x_{1}+f}{f x_{1}}+\frac{1}{x_{2}}$

So we get focal length as $x_{1}+x_{2}$