Question

The number of waves in a glass slab of thickness $4$ cm is the same as in a water column of height $5$ cm, when the same monochromatic ray of light travels through them. What is the refractive index of water if the refractive index of glass is $\frac{5}{3}$?

• A. $1.25$
• B. $1.5$
• C. $1.33$
• D. $1.75$

Answer 1

The correct option is A $1.25$

Given thickness of glass slab=4 cm and height of water column=5 cm

and refractive index of glass ${\mu }_g$ =$\frac{5}{3}$

As number of waves is equal in both the glass and water medium with according to their height and thickness, we can

say $\frac{{\mu }_w}{{\mu }_g}=\frac{v_g}{v_w}=\frac{\frac{thicknessofglass}{time}}{\frac{heightofwatercolumn}{time}}$

$\frac{{\mu }_w}{{\mu }_g}=\frac{4}{5}{\mu }_w=\frac{4}{5}\times \frac{5}{3}=\frac{4}{3}$