Find the position of an object which when placed

Asked by admin @ 17/08/2021 in Science viewed by 320 People

find the position of an object when placed in front of a concave mirror of focal length 20 cm produces a virtual image,which is twice size of object.

Answered by admin @ 17/08/2021

Answer:

The image is at distance of 20 cm from the mirror on the side opposite to that of object.

Explanation:

Given,

f = −20 and M = 2

We know that ;

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

= $\frac{1}{v}= \frac{1}{f} - \frac{1}{u} = \frac{u-f}{uf}$

= $v = \frac{uf}{u-f}$

We know,

M = - $\frac{v}{u}$

Substituting the value of v ,

M = - $\frac{f}{u-f}$

Substituting value of f = 20

M = $\frac{20}{u+20}$

According to question,

M = 2

$\frac{20}{u+20}$ = 2

⇒20 = 2u + 40

⇒ u = − 10.

⇒ $v = \frac{uf}{u-f}$

⇒ $v = \frac{10*20}{-10+20}$ = 20

Hence,

The image is at distance of 20 cm from the mirror on the side opposite to that of object.

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