Question

What is meant by the statement “the critical angle for diamond is\[{24^0}\] “ ?

Answer 1

Hint: This question is based on the concept of total internal reflection and critical angle. The critical angle is the angle of incidence of a light ray travelling from the denser medium to the rarer medium such that the angle of refraction in the rarer medium will be equal to ${90^0}$

Complete step-by-step solution:

The statement “the critical angle for diamond is\[{24^0}\] “ means that when the light ray is travelling from diamond to air, the angle of incidence is \[{24^0}\]for which the angle of refraction will be ${90^0}$ as shown in the figure $\left( b \right)$
Also, If angle of incidence is greater than \[{24^0}\] the ray of light will undergo total internal reflection as shown in figure $\left( c \right)$ and hence diamond shines.
The refractive index of the diamond can be calculated by,
$\mu = \dfrac{1}{{\operatorname{Sin} C}}$ ……….. $\left( 1 \right)$
Where, $\mu = $ refractive index of the material.
$C = $ Critical angle
Substituting the critical angle as ${24^0}$ we get refractive index as
$\mu = \dfrac{1}{{\operatorname{Sin} 24}}$
$\mu = \dfrac{1}{{0.407}}$
Therefore, refractive index of diamond $\mu = 2.4$
Additional information:
Case (i) When angle of incidence less than critical angle $\left( {i < c} \right)$
When the ray of light travels from denser medium to rarer medium and if angle of incidence lesser than critical angle, the ray of light will undergo refraction as shown in figure $\left( a \right)$ .
Case (ii) ) When angle of incidence is equal to critical angle $\left( {i = c} \right)$
When the ray of light travelling from denser medium to rarer medium and if angle of incidence is equal to critical angle then ray of light will undergo refraction with angle of refraction ${90^0}$ as shown in figure $\left( b \right)$.
Case (iii) When angle of incidence less than critical angle $\left( {i > c} \right)$
When the ray of light travels from denser medium to rarer medium and if angle of incidence greater than critical angle, the ray of light will undergo total internal reflection as shown in figure $\left( c \right)$ .

Note: It should be noted that for the ray of light to undergo total internal reflection the ray of light should travel from denser medium to rarer medium and also the refractive index is a dimensionless quantity that is it does not have any unit.