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  4. 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:

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Q. 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:

JIPMERJIPMER 1999

Solution:

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} $