Question

For the same angle of incidence ,the angle of refraction in media P,Q,R and S are\[{{50}^{0}}\],${{40}^{0}}$,${{30}^{0}}$,${{20}^{0}}$,respectively. The speed of light is minimum in medium:
A) P
B) Q
C) R
D) S

Answer 1

Hint: The law of reflection gives a relationship between reflected light and incident light and the angle of emergence is the angle of light coming out of a medium .The first medium may be air and the medium which is in the middle may be water or a glass slab. Refractive index of water is 1.333 and the refractive index of glass is 1.003.

Complete answer:
Snell's law is used to describe the relationship between refraction and angle of incidence. Snell's law which is defined as the ratio of the sines of the angles of incidence and refraction is equal to the ratio of phase velocities and is also equal the reciprocal of the ratio of the indices of refraction given by:
\[\dfrac{\sin {{\theta }_{2}}}{\sin {{\theta }_{1}}}=\dfrac{{{v}_{2}}}{{{v}_{1}}}=\dfrac{{{n}_{1}}}{{{n}_{2}}}\]
Velocity of light in any medium is:
$v=\dfrac{c}{n}$ $\cdots \cdots (1)$
Where n= medium’s index of refraction,
C=velocity of light in air
$c=f\lambda $
Where f=frequency
$\lambda $= wavelength
$v=\dfrac{f\lambda }{n}$
Wavelength is defined as the distance between two crests or troughs of wave .SI unit of wavelength is meter (m) and SI unit of frequency is hertz (z).
Refractive index is dimensionless .
By the Snell's law of refraction;
$\dfrac{\sin {{\theta }_{2}}}{\sin {{\theta }_{1}}}=n$ $\cdots \cdots (2)$
Substituting equation (1) in equation (2)
On substituting
$v=\dfrac{c\times \sin {{\theta }_{1}}}{\sin {{\theta }_{2}}}$
where${{\theta }_{2}}$ is a constant
$v\propto \sin {{\theta }_{1}}$
In the medium S the value of ${{\theta }_{1}}={{20}^{0}}$
Which is minimum
So in the medium S the value of v is also minimum.

Option D is correct.

Note:
Students the velocity of light in any medium is directly proportional to$\sin {{\theta }_{1}}$. Refractive index is different for different mediums and velocity of light is also different for different mediums. The medium can be air, diamond, glass and water. The speed of light is \[3\times {{10}^{8}}m{{s}^{-1}}\] and SI unit of velocity is meter per second ($m{{s}^{-1}}$).