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Question

A concave mirror produces 3 times enlarged image of am object play at 10cm in front of it. Calculate the radius of curvature for the mirror.

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Solution

The mirror produces three times enlarged image. So, magnification(m) = 3 WE KNOW, magnification of spherical mirrors = m = -v/u Where v is the distance between image and mirror and u is the distance between object and mirror. Here, u = -10 cm => 3 = -V/-10 =>v = 30 So , the distance between image and mirror = 30 cm 1/v + 1/u = 1/f(mirror formula) 1/30 + 1/-10 = 1/f 1/30 - 1/10 = 1/f -2/30 = 1/f -1/15 = 1/f f = -15 cm We know radius of curvature = 2f So, radius of curvature = R = 2*-15 = -30 cm which is the required answer. SHORTCUT - Remember the formula, m = f/(f-u) So, 3 = f/(f-(-10)) 3 = f/(f+10) Cross multiply, 3f + 30 = f 2f = -30 R = -30 cm (R= 2f)

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