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Question

The curvature radii of a concavo-convex glass lens are 20 cm and 60 cm. The convex surface of the lens is silvered. With the lens horizontal, the concave surface is filled with water. The focal length of the effective mirror is (μ of glass =1.5,μ of water =4/3)

A
9013 cm
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B
2013 cm
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C
36080 cm
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D
36043 cm
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Solution

The correct option is D 36043 cm

Focal length of the equivalent mirror can be given by
1feq=1fm2[1f1+1f2]

where f1 is the focal length of the plano concave lens of water, f2 is the concavo-convex lens of glass and fm is the focal length of the mirror formed due to silvering of the outside surface

fm=10 cm

1f1=(431)[1(160)]=1180

1f2=(321)[160(120)]=160

1feq=1102[1180+160]=1390

feq=9013 cm

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