Question

A glass slab of thickness 4 cm contains same number of waves as 5 cm thickness of water, when both are traversed by the same monochromatic light. If the refractive index of water is 4/3, what is the refractive index of glass:

• A. 5/3
• B. 5/4
• C. 16/5
• D. 1.5

Answer 1

Answer: (A)

Suppose $x$ is the number of waves contained in both. The wavelength of light in glass $=4\text{/}x$ The wavelength of light in water $=5\text{/}x$ We know that refractive index is inversely proportional to wavelength of light $\mu \propto \frac{1}{\lambda }$ hence, ${\mu }_g{\lambda }_g={\mu }_{\omega }{\lambda }_{\omega }$ ${\mu }_g\frac{4}{x}=\frac{4}{3}\cdot \frac{5}{x}\Rightarrow {\mu }_g=\frac{5}{3}$