Question

The radius of curvature of a concave mirror is 40 cm. Find position of an object in front of the mirror, so
that its real image is two times the size of the object.

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Answer 1

Explanation:

Answer refer in Attachment.

Thank you

Answer 2

Answer:

The position of an object in front of the mirror is 30cm from the mirror.

Explanation:

Given that:

the radius of the curvature of concave mirror $R= 40cm$

The focal length  $f=\frac{R}{2}=\frac{40}{2}=-20cm$          (by the convention)

Given   $m=-2$

Magnification   $m = \frac{-v}{u}$

                       $-2=\frac{-v}{u} \\ v=2u$

From the mirror formula:

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

             $\frac{1}{-20}=\frac{1}{2u}+\frac{1}{u}$

⇒            $\frac{-1}{20}=\frac{3}{2u}$

  ∴          $2u=-60\\ u=-30$

Therefore the position of object is 30cm in front of the mirror.