Question

Draw the ray diagram of a glass slab having medium A and B for the velocity of light ray V_A and V_B respectively and define Snell's law.

1. If V_B = 1.5 V_A, then which medium is denser?
2. What is the refractive index of A with respect to B?
3. What is the refractive index of B with respect to A?

Answer 1

Where i = angle of incidence,

r = angle of refraction,

e = angle of emergence

At point N, using snell's law

_Aη_B = ${\displaystyle \frac{\sin \text{i}}{\sin \text{r}}}$ = constant

According to snell's law, the sin i of the angle of incidence to the sin r of the angle of refraction is always constant.

1. Medium A is denser.
2. Refractive index of A with respect to B is:
   _Bη_A = ${\displaystyle \frac{{\text{V}}_{\text{B}}}{{\text{V}}_{\text{A}}}=\frac{1.5{\text{V}}_{\text{A}}}{{\text{V}}_{\text{A}}}=\frac{3}{2}}$
3. Refractive index of B with respect to A is:
   _Aη_B = ${\displaystyle \frac{1}{{}_{\text{B}}{\eta }_{\text{A}}}=\frac{2}{3}}$