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. 44684
• B. 44685
• C. 16-May
• D. 1.5

Answer 1

Answer: (A)

44684

Answer 2

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, ${{\mu }_{g}}{{\lambda }_{g}}={{\mu }_{\omega }}{{\lambda }_{\omega }}$ ${{\mu }_{g}}\frac{4}{x}=\frac{4}{3}\cdot \frac{5}{x}\,\,\,\,\Rightarrow \,\,\,{{\mu }_{g}}=\frac{5}{3}$