Question

a spherical mirror produces a magnification of -1 on a screen placed at a distance of 40cm from the mirror i) write the type of mirror ii) What is the focal length of the mirror

Answer 1

Answer:

f =-20 cm

Explanation:

Given that,

The magnification of a spherical mirror, m = -1

The image distance, v = 40 cm (for negative magnification)

The magnification of a concave mirror is negative. The mirror showing -1 magnification is a concave mirror.

Let f be the focal length of the mirror. We know that,

$m=\dfrac{-v}{u}\\\\-1=\dfrac{-v}{u}\\\\v=u$

Object distance, u = -40 cm

Using mirror's formula i.e.

$\dfrac{1}{f}=\dfrac{1}{u}+\dfrac{1}{v}\\\\f=\dfrac{1}{\dfrac{1}{-40}+\dfrac{1}{-40}}\\\\f=-20\ cm$

So, the focal length of the mirror is 20 cm.