Question

What is the focal length of a concave mirror that magnifies, by a factor of +3.2 an object that is placed 30 cm from the mirror?

Answer 1

1/o + 1/f = 1/i 

In this case o = 30 

and, i / o = 3.2 
then i = 96 

by substituting , 
we can get f = 44

Answer 2

The object placed at varying distances from the focal point accounts for the change in focal length.

And the focal length of a concave mirror is 44 cm.

What is focal length?

When a mirror or lens is placed at some distance from the focal point, then that distance is known as the focal length of the mirror or lens.

Given data:

The magnification of the image is, m = + 3.2.

The object distance is, u = 30 cm.

The expression for the magnification of the image is ,

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

Here,

v is the image distance.

Solving as,

$3.2 = \dfrac{v}{30}\\\\v =3.2 \times 30\\\\v = 96 \;\rm cm$

Now, using the mirror equation to calculate the focal length of the concave mirror is,

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

Solve by substituting the values as,

$\dfrac{1}{f}=\dfrac{1}{96}+\dfrac{1}{30}\\\\\\\dfrac{1}{f}=\dfrac{30+96}{2880}\\\\f =44 \;\rm cm$

Thus, we can conclude that the focal length of a concave mirror is 44 cm.

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