Question

An object is 5 cm high is placed at a distance of 10 cm from a concave mirror of radius of curvature 30 cm. Find the size of the image.
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Answer 1

Given :-

Object distance (u) = -10cm

Radius (R) = 30cm

Height of object (h) = 5cm

Size of image = ?

Also,

Focal length (F) = R/2

= 30/2

= -15cm

Solution :-

Mirror formula = 1/v +1/u = 1/f

Or,

1/v = 1/u - 1/f

1/v = -1/5 - (-1/15)

1/v = -1/5 + 1/15

1/v = (-3 + 1)/15

1/v = -2/15

v = -7.5 cm

Magnification = -v/u

= -(-7.5)/(-5)

= -(7.5)/5

= -1.5 cm

Also, Magnification = h'/h

h' = size of image

h = size of object

M = -1.5

-1.5 = h'/5

h' = -1.5 x 5

h' = -7.5

(i) Size of image is 7.5cm.

(ii) As M ∠ 0, image is magnified and inverted.