Question

The radius of curvature of a concave mirror is 40 cm. Find position of the real image of an object in front of the mirror, so that its magnification is -2.
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Answer 1

GIVEN

• Radius of Curvature (R) = -40 cm
• Magnification (m) = -2

TO FIND

• Image position

SOLUTION

• m = -v/u
• -2 = -v/u
• 2 = v/u
• v = 2u
• u = v/2 _(i)

Using Mirror formula ⇒1/f = 1/v + 1/u

• 1/v = 1/-20 + 2/v
• 1/v = (-v + 20(2))/20v
• 1/v = (-v + 40)/20v
• 20v/v = -v + 40
• 20 = -v + 40
• v = 40 - 20
• v = 20 cm

∴ Image is formed at 20 cm from mirror.