Question

Mirages are observed in deserts due to the phenomenon of
A. Interference of light and reflection of light.
B. Total internal reflection of light and refraction of light
C. Scattering of light and dispersion of light
D. Double refraction of light

Answer 1

Hint: First under each phenomenon given in the options and try to figure out which can cause mirages in deserts. Maybe the high temperature of deserts helps in this process.
Formula used:
${\mu }_i\sin i={\mu }_r\sin r$

Complete step-by-step answer:

Mirages are observed in deserts due to the phenomenon of total internal reflection of light and refraction of light.
When a light ray passes from a denser medium to a rarer medium (for example, from glass to air), the ray bends away from the normal at the interface of the two mediums. Sometimes the bending is so much that it gets reflected into the same medium, where it was incident.
This phenomenon can be explained by Snell’s law. Snell’s law gives us the relation between the refractive indices of the two given mediums and the angles made by the light ray with the normal at the interface (i.e. that angle of incidence and the angle of refraction). Snell’s law is given as ${\mu }_i\sin i={\mu }_r\sin r$, where ${\mu }_i$ and ${\mu }_r$ are the refractive indices mediums where the light ray is incident and refracted respectively and i and r are the angles of incidence and refraction respectively.
Suppose a light ray passes through a denser medium to a rarer medium as shown. Let angle of incidence be such that the ray after incidence refracts at the extent that it passes through the interface as shown.
 

By using Snell’s law we get, ${\mu }_i\sin i={\mu }_r\sin r$. In this case, r will equal to 90 degrees. Therefore,
 ${\mu }_i\sin i={\mu }_r\sin (90)$ and we know that sin 90=1
$\Rightarrow {\mu }_i\sin i={\mu }_r.1$
$\Rightarrow \sin i={\displaystyle \frac{{\mu }_r}{{\mu }_i}}\Rightarrow i={\sin }^{-1}\left({\displaystyle \frac{{\mu }_r}{{\mu }_i}}\right)$.
This value of i is called critical angle (${\theta }_c$). If the angle of is more than ${\theta }_c$, the incident light ray will be reflected instead of refraction. This is called total internal reflection.
This is what happens in deserts. Light rays from far distant scenery fall at the sand and total internal reflection followed by refraction takes place.
Due to intense heat, the sand (ground) becomes rarer than the air just above the ground. Therefore, light from air just above the ground, when fall on the ground, gets reflected because the angle of incidence is more than ${\theta }_c$. Due to the temperature differences in the layers of air, the light is refracted.

Note: Total internal reflection can only take place when a light ray passes through a denser medium to a rarer medium. If the light ray passes from a rarer medium into a denser medium, the ray will always bend towards the normal and will never be reflected into the same medium.