Question

Magnification of an image is -2 and an object is
placed at a distance of 20cm from a concave
mirror then find the focal length of the mirror​

Answer 1

Given :

In concave mirror,

Magnification of image = -2

Object distance = - 20cm

To find :

The focal length of the mirror

Solution :

Firstly we have to find image distance using magnification formula that is,

The Magnification produced by a mirror is equal to the ratio of the image distance to the object distance with a minus sign .i.e.,

$\boxed{ \bf m = - \dfrac{v}{u} }$

where,

• v denotes image distance
• u denotes object distance

by, substituting all the given values in the formula,

$\dashrightarrow \sf m = - \dfrac{v}{u}$

$\dashrightarrow \sf - 2 = - \dfrac{v}{20}$

$\dashrightarrow \sf v = 2 \times 20$

$\dashrightarrow \sf v = 40 \: cm$

Now, using mirror formula that is,

» A formula which gives the relationship between image distance, object distance and focal length of a sperical mirror is known as the mirror formula .i.e.,

$\boxed{\bf \dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}}$

where,

• v denotes Image distance
• u denotes object distance
• f denotes focal length

now, substituting all the given values,

$\dashrightarrow\sf \dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}$

$\dashrightarrow\sf \dfrac{1}{f} = \dfrac{1}{( - 40)} + \dfrac{1}{( - 20)}$

$\dashrightarrow\sf \dfrac{1}{f} = \dfrac{1}{( - 40)} - \dfrac{1}{ 20}$

$\dashrightarrow\sf \dfrac{1}{f} = \dfrac{ - 1 - 2}{ 40}$

$\dashrightarrow\sf \dfrac{1}{f} = \dfrac{ -3}{ 40}$

$\dashrightarrow\sf f = - \dfrac{40}{3}$

$\dashrightarrow\sf f = - 13.3 \: cm$

Thus, the focal length of the mirror is 13.3cm