Question

The refractive index of glass is $3/2,$ The time taken by a monochromatic light ray to travel distance in air is 4 s. The time taken by the light ray to travel the same distance in glass is
(A) 4 s
(B) 6 s
(C) 8/3 s
(C) 3 s

Answer 1

Hint: We know that in physics, refraction is the change in direction of a wave passing from one medium to another or from a gradual change in the medium. Refraction of light is the most commonly observed phenomenon, but other waves such as sound waves and water waves also experience refraction. Laws of refraction state that: The incident ray, reflected ray and the normal, to the interface of any two given mediums; all lie in the same plane. The ratio of the sine of the angle of incidence and sine of the angle of refraction is constant.

Complete step by step answer:
We can solve this question using the relation ${\displaystyle \frac{{\mathrm{v}}_1}{{\mathrm{v}}_2}}={\displaystyle \frac{{\mu }_2}{{\mu }_1}}$
where ${\mathrm{v}}_1$ and ${\mathrm{v}}_2$ are the respective velocity of light in air and glass and ${\mu }_1$ and ${\mu }_2$ are the respective refractive index of air and glass.
Given: ${\mu }_2={\displaystyle \frac{3}{2}}$ and ${\mu }_1=1$
Time taken by light to travel a distance $x$ in air $4s$ and that in glass be $t$.
$\Rightarrow {\displaystyle \frac{{\displaystyle \frac{\text{x}}{4}}}{{\displaystyle \frac{\text{x}}{\text{t}}}}}={\displaystyle \frac{{\displaystyle \frac{3}{2}}}{1}}$
Or we can write the expression as:
${\displaystyle \frac{\text{t}}{4}}={\displaystyle \frac{3}{2}}$
This can be written as $t=6$ s.

Hence, the correct option is option B.

Note We know that refraction is an effect that occurs when a light wave, incident at an angle away from the normal, passes a boundary from one medium into another in which there is a change in velocity of the light. The wavelength decreases as the light enters the medium and the light wave changes direction. Reflection involves a change in direction of waves when they bounce off a barrier. Refraction of waves involves a change in the direction of waves as they pass from one medium to another. Refraction, or the bending of the path of the waves, is accompanied by a change in speed and wavelength of the waves. The refractive index measures the phase velocity of light, which does not carry information. The phase velocity is the speed at which the crests of the wave move and can be faster than the speed of light in vacuum, and thereby give a refractive index below 1.