Question

An object is placed in front of a convex mirror of focal length 20cm.The magnification is found to be ¼.Find the location of the object.

Answer 1

Answer:

Explanation:

We know,   1/v+1/u=1/f

1/4+1/u=1/20

1/u=1/20-1/4

1/u=(1-5)/20

1/u=-4/20

1/u=-1/5

1/u=-0.2cm

The location of the object=0.2cm

Hope it helps

Answer 2

Answer:

The position of the object is -60cm.

Explanation:

Given:

Focal length (f) = 20cm

Magnification (M) = 1/4

To find:

Location of the object (u) =?

Formula:

M = -v/u

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

Solution:

It is given that the magnification is 1/4. Therefore,

$\frac{1}{4} = -\frac{v}{u}$

$v= -\frac{1}{4}u$

Hence, we get the image to be 1/4 of the object.

Substituting the values in the lens maker formula, we get

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

$\frac{1}{f} = \frac{1}{-\frac{1}{4}u} + \frac{1}{u}$

$\frac{1}{20} = -\frac{4}{u} + \frac{1}{u}$

$\frac{1}{20} = \frac{-3}{u}$

$u = -3 * 20$

u = -60cm

Therefore, the location of the object is -60cm.

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