A convex lens of focal length 0.15 m is made of material of refractive index `3/2`, When it is place4 in a liquid, its focal length is increased by 0.225 m. The refractive index of the liquid is

Options

A. `7/4`
B. `5/4`
C. `9/4`
D. `3/2`

Answer

B

Explanation

From Lens formula,
Focal length of lens in air, `1/f_(a) =-(mu_(g)/(mu_(a))-1)(1/R_(1) – 1/R_(2))`
Focal length of lens in water`1/f_(l) =-(mu_(g)/(mu_(l))-1)(1/R_(1) – 1/R_(2))`
`therefore(1/f_(a))/(1/f_(l)) =(mu_(g)/(mu_(a)-1))/(mu_(g)/(mu_(l)) -1)`
`implies f_(2)/(f_(a))=((mu_(2)-1)mu_(1))/(3/2 – mu_(1))`
`implies 0.375/0.15 = (1/2 mu_(1))/(3/2-mu_(1))`
On solving we get, `mu_(1)=5/4`