Question

A convex thin lens with refractive index of 1.50 has a focal length of 30cm in air. When immersed in a certain transparent liquid, it becomes a negative lens of focal length of 188 cm. Determine the refractive index of the liquid.

Answer 1

`n_l = 1.97`

Step-by-step explanation:

given data:

refractive index of lens 1.50

focal length in air is 30 cm

focal length in water is -188 cm

Focal length of lens is given as

`(1)/(f) =(n_2 -n_1)/(n_1) * \left [(1)/(r1) -(1)/(r2)   \right ]`

`(1)/(f) =(n_(g) -n_(air))/(n_(air)) * \left [(1)/(r1) -(1)/(r2)   \right ]`

`(1)/(f) =(n_(g) -1)/(1) * \left [(1)/(r1) -(1)/(r2)   \right ]`

focal length of lens in liquid is

`(1)/(f) =(n_(g) -n_(l))/(n_(l)) * \left [(1)/(r1) -(1)/(r2)   \right ]`

`=(n_(g) -n_(l))/(n_(l))  [(1)/((n_(g) - 1) f)`

rearrange fro
`n_l`

`n_l = (n_g f_l)/(f_l+f(n_g-1))`

`n_l = (1.50*(-188))/(-188 + 30(1.50 -1))`

`n_l = 1.97`