Question

An object is 20 cm from a concave mirror of radius of curvature 60 cm

Answer 1

The position and nature of the image are magnified,

What is the focal length?

Focal length, usually represented in millimeters (mm), is the basic description of a photographic lens.

Radius of curvature of the mirror, R = -60 cm

Focal length of the mirror, f = -30 cm

Object distance, u = -20 cm

Let v is the position of the mirror. It can be calculated as :

$\rm \dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}\\\\\dfrac{1}{v}=\dfrac{1}{f}-\dfrac{1}{u}\\\\\dfrac{1}{v}=\dfrac{1}{-30}-\dfrac{1}{-20}\\\\\\\dfrac{1}{v}=\dfrac{-20 - (-30)}{(-30)(-20)}\\\\\dfrac{1}{v}=\dfrac{10}{(-30)(-20)}\\\\\dfrac{1}{v}=\dfrac{10}{600}\\\\\dfrac{1}{v}=\dfrac{1}{60}\\\\v=60$

The image is formed at a distance of 60 cm behind the concave mirror.

$\rm m=\dfrac{-v}{u}\\\\m=\dfrac{-60}{-30}\\\\m=2$

The image is magnified.

Hence, the position and nature of the image are magnified,

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