The power of a biconvex lens is 10 dioptre and the radius of curvature of each surface is 10 cm. Then the refractive index of the material of the lens is

Options

A. `(3)/(2)`
B. `(4)/(3)`
C. `(9)/(8)`
D. `(5)/(3)`

Answer

A

Explanation

Power of lens, P (in diopter)
`=(100)/("focal length" f ("in" cm))`
`:.f=(100)/(10)=10 cm`
According to lens maker.s formula
`(1)/(f)=(mu-1)((1)/(R_(1))-(1)/(R_(2)))`
For biconvex lens, `R_(1)=+R, R_(2)=-R`
`:.(1)/(f)=(mu-1)((1)/(R_(1))+(1)/(R_(2)))implies(1)/(f)=(mu-1)((2)/(R))`
`:.(1)/(10)=(mu-1)((2)/(10))impliesmu=(1)/(2)+1=(3)/(2)`