A thin lens made of glass (refractive index = 1.5) of focal length f= 16 cm is immersed in a liquid of refractive index 1.42. If its focal length in liquid is `f_1`, then the ratio `f_1`lf is closest to the integer

Options

A. 9
B. 17
C. 1
D. 5

Answer

A

Explanation

According to Lens maker.s formula in air,
`(1)/(f_a)=((mu_g)/(mu_a)-1)[(1)/(R_1)-(1)/(R_2)]`
In liquid medium,
`(1)/(f_L)=((mu_g)/(mu_L)-1)((1)/(R_1)=(1)/(R_2))`
`therefore(f_a)/(f_L)=((mu_g)/(mu_L)-1)/((mu_g)/(mu_a)-1)=(mu_g-mu_L)/(mu_g-mu_a)xx(mu_a)/(mu_L)`
`=(1.5-1.42)/(1.5-1.0)xx(1)/(1.42)`
`=(0.08)/(0.5)xx(1)/(1.42)`
`therefore(f_L)/(f_a)=(0.71)/(0.08)`
`=8.875~~9`