Find the size , nature and position of image formed when an object of size 1 cm is placed at a distance of 15 cm from a concave mirror of focal length 10 cm

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Solution

Object height (h) = 1cm
Object distance (u) = -15 cm [Object distance and focal length are taken negative in Concave mirror;New Cartesian Sign Convension]

Focal length (f) = -10 cm

We know, 1/v + 1/u = 1/f [Mirror formula]

Therefore, 1/v = 1/f - 1/u

1/v = 1/(-10) - 1/(-15)

1/v = 1/(-10) + 1/15 [(-) x (-) = (+)]

1/v = 5/(-150) [Cross-multiplying]

v = -150/5 = -30 cm

Image is -30 cm in front of mirror.

m = h'/h = -v/u [Formula of magnification]

Therefore,h' = -vh/u

h' = -(-30) x (1)/(-15)

h' = -2 cm

Image is real,inverted and enlarged.

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