Question

A concave mirror produces a real, four times magnified image of an object placed at 10cm infront of it.Find the position of the image and the radius of curvature of the mirror.

Answer 1

Answer:

1. Left of the mirror .

2 . R = 16 cm.

Explanation:

Given :

Object distance ( u ) = 10 cm .

Four times magnified image of an object i.e.  $\displaystyle{m_2/m_1=4}$

We know :

$\displaystyle{m=-\frac{v}{u} }\\\\\\\displaystyle{4=-\frac{v}{10} }\\\\\\\displaystyle{}v=-40 \ cm}$

Hence the position of image is same of object  [ Left side ] .

Now , we have mirror formula :

$\displaystyle{\dfrac{1}{f}=\dfrac{1}{u}+\dfrac{1}{v}}\\\\\\\displaystyle{\dfrac{1}{f}=\dfrac{1}{-10}+\dfrac{1}{-40}}\\\\\\\displaystyle{\dfrac{1}{f}=\dfrac{-1-4}{40}}\\\\\\\displaystyle{\dfrac{1}{f}=\dfrac{-5}{40}}\\\\\\\displaystyle{f=-8 \ cm}$

Negative sign show only direction :

We can write f = 8

We know   R = 2 f

R = 16 cm .

Thus radius of curvature of the mirror is 16 cm .

Answer 2

Answer:

A concave mirror produces a real.

four times magnified image of an object placed at 10cm in front.

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