Question

A plate of glass with parallel faces having a refractive index of 1.57 is resting on the surface of water in a tank. A ray of light coming from above in air makes an angle of incidence 37.5 ∘∘ with the normal to the top surface of the glass.What angle does the ray refracted into the water make with the normal to the surface? Use 1.33 for the index of refraction of water.

Answer 1

Answer:

$27.26^{\circ}$

Step-by-step explanation:

We are given that

$n_g=1.57$

$n_w=1.33$

Angle of incidence,i=37.5 degree

We have to find the angle of refraction into the water made by ray wit the normal to the surface.

Refractive index of water,$n_a=1$

By Snell's law

$\frac{n_g}{n_a}=\frac{sin i}{sin r}$

$sin r=\frac{n_a sini}{n_g}=\frac{1\times sin37.5}{1.57}$

$sin r=0.388$

$r=sin^{-1}(0.388)=22.83^{\circ}$

Again for glass water surface

Using Snell's law

Angle of incidence,i'=22.83 degree

$\frac{n_w}{n_g}=\frac{sin i}{sin r}$

$\frac{1.33}{1.57}=\frac{sin22.83}{sin r'}$

$sin r'=\frac{1.57sin(22.83)}{1.33}=0.458$

$r'=sin^{-1}(0.458)=27.26^{\circ}$