Question

An object of height 2 cm is placed at a distance 20 cm in front of a concave mirror of focal length 12 cm. Find the position, size and nature of the image.

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Answer

Object height (O) = 2 cm

Focal length (f) = 12 cm (negative)

Object distance (u) = 20 cm (negative)

1\over u + 1\over v = 1\over f

⇒ – 1\over 20 + 1\over v = – 1\over 12

1\over v = – 1\over 12 + 1\over 20

1\over v = -5 + 3\over 60

1\over v = – 2\over 60

1\over v = – 1\over 30

⇒ v = – 30 cm

Hence, the image is formed at a distance of 30 cm in front of the mirror.

Image\ size\over object\ size=Image\ distance\over object\ distance

I\over 2=-30\over 20

⇒ I = {30\over 20} × 2 = – 3 cm

Hence, the length of the image = 3 cm

The image will be real, inverted and magnified.

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