Question

# An object is placed exactly midway between a concave mirror of radius of curvature 40cm and a convex mirror of radius of curvature 30cm. The mirrors face each other and are 50cm apart. Determine the nature and position of the image formed by successive reflections first at the concave mirror and then at the convex mirror.

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Solution

## Given: An object is placed exactly midway between a concave mirror of radius of curvature 40cm and a convex mirror of radius of curvature 30cm. The mirrors face each other and are 50cm apart. To find the nature and position of the image formed by successive reflections first at the concave mirror and then at the convex mirror.Solution:For concave mirror,As per the given condition,object distance, u=25cm, as the mirrors are 50cm apart.Radius of curvature, R=40cmSo the focal length, f=R2=402=20cmApplying lens formula, we get1f=1v+1u⟹1v=1f−1u⟹1v=120−125⟹1v=5−4100⟹v=100cmTherefore the image is 100cm behind the concave mirror.Magnification, m1=−vu=−10025=−4Hence the image formed by the concave mirror is inverted, virtual and enlarged.This becomes object for convex mirror, soobject distance, u′=−(100−50)=−50cmRadius of curvature of convex mirror, r=30cmSo the focal length, f′=r2=302=−15cmApplying lens formula, we get1f′=1v′+1u′⟹1v′=1f′−1u′⟹1v′=1−15−1−50⟹1v′=−10+3150⟹v=−21.4cmHence the position of the final image is 21.4 behind the convex mirror.Magnification, m2=−v′u′=−−21.4−50=−0.43So the nature of the final image formed is inverted of inverted, i.e., upright.

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