Q. A glass slab of thickness 8 cm contains the same number of waves as 10 cm of water when both are transverse by the same monochromatic light. If the refractive index of water is 4/3, then refractive index of glass is

A) 5/4
B) 3/2
C) 5/3
D) 16/15
Explanation

(c) Let the wavelength of monochromatic light in glass be $\lambda_{g}$cm and in water be $\lambda_{w}$cm.
$\therefore$ Number of waves in 8 cm of glass=$\frac{8}{\lambda_{g}}$, and number of waves in 10 cm of glass $= \frac{8}{\lambda_{w}}$.
$\frac{8}{\lambda_{g}} = \frac{10}{\lambda_{w}}\ or\frac{\lambda_{w}}{\lambda_{g}} = \frac{10}{8} = \frac{5}{4}$
Now, $\mu_{g} = \frac{c}{v_{g}}\ and\ \mu_{w} = \frac{c}{v_{w}}$
$\therefore\ \ \frac{\mu_{g}}{\mu_{w}} = \frac{v_{w}}{v_{g}} = \frac{v\lambda_{w}}{v\lambda_{g}} = \frac{5}{4}$
$\mu_{g} = \frac{5}{4}\mu_{w} = \frac{5}{4} \times \frac{4}{3} = \frac{5}{3}$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

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