The two surfaces of a 1 biconvex lens has same radii of curvatures. This lens is made of glass of refractive index 1.5 and has a focal length 10 cm in air. The lens is cut into two equal halves along a plane perpendicular to its principal axis to yield two plano-convex lenses. The two pieces are glued such that combination lens is immersed in water (refractive index = `4/3`), its focal length (in cm) is

Options

A. 5
B. 10
C. 20
D. 40

Answer

D

Explanation

A Biconvex lens is divided into two parts then the focal length of each part becomes 2f.
Then, the effective focal length of a biconvex lens is given by,
`1/F = 1/(2f) +1/(2f)`
`impliesF=f`
The focal length of lens in air and water is given by,
`1/f_(air) = (mu_(g)-1)(1/R_(1) -1/R_(2)) …..(1)`
`1/f_(water) = ((mu_(g)-1)/mu_(v))(1/R_(1) -1/R_(2)) …..(2)`
Dividing equation (1) by (2), we get,
` F_(water)/(f_(air))=(mu_(w)[mu_(g)-1])/(mu_(R)-mu_(w))=(4/3 [3/2 -1])/(3/2 – 4/3) =4`
`therefore F_(water)= 4 xx 10=40cm`