Question

# A convex lens of radii of curvature 20 cm and 30 cm respectively. It is silvered at the surface which has smaller radius of curvature. Then it will behave as (μg=1.5)

A
concave mirror with equivalent focal length 3011cm
B
concave mirror with equivalent focal length 6011cm
C
convex mirror with equivalent focal length 3011cm
D
convex mirror with equivalent focal length 6011cm
Solution
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#### Focal length for lens, 1fL=(μg−1)[1R1−1R2]Here, μg=1.5,R1=20cm,R2=−30cm∴1fL=(1.5−1)[120−1−30]=0.5×or fL=1205=24cmFocal length for mirror, fm=R2=−202=−10cm∴ Equivalent focal length feq=−2fL+1fm=−224+1−10=−1160⇒feq=−6011cmHence, this system behaves like a concave mirror of local length −6011 cm.

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