Question

Speed of light in air is $3\times {10}^{8}m/s$ and speed of light in common glass is $2\times {10}^{8}m/s$.Calculate the refractive index of glass.

Answer 1

Step 1. Given data

1. Speed of light in air is $3\times {10}^{8}m/s$
2. Speed of light in common glass is $2\times {10}^{8}m/s$

Step 2. Formula used

Refractive index of medium $B$ with respect to medium $A$ , ${\mathrm{\eta }}_{BA}=\frac{\mathrm{Speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{medium}\mathrm{A}}{\mathrm{Speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{medium}\mathrm{B}}$ , that is when light travel from medium $A$ to medium $B$

Step 3. Find the refractive index of glass.

Refractive index of glass, with respect to air is ${\mathrm{\eta }}_{\mathrm{glass}}=\frac{\mathrm{Speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{vacuum}}{\mathrm{Speed}\mathrm{of}\mathrm{light}\mathrm{in}\mathrm{glass}}=\frac{3\times {10}^8}{2\times {10}^8}=\frac{3}{2}=1.5$

Hence, the refractive index of glass is $1.5$.