Question

Determine the refractive index of benzene if critical angle is \[{42^o}\].

Answer 1

Hint the critical angle is defined as the angle of incidence that provides an angle of refraction of 90-degrees. Make particular note that the critical angle is an angle of incidence value. The actual value of the critical angle is dependent upon the combination of materials present on each side of the boundary.

Complete step-by-step answer:
 The relation between refractive index and critical angle is given by:
\[C = {\sin ^{ - 1}}(\dfrac{1}{\mu })\]
Where
\[C\] is the critical angle
\[\mu \] refractive index of the substance.
Now putting the values given values in the equation
\[\sin ({42^o}) = \dfrac{1}{\mu }\]
\[\mu = \dfrac{1}{{\sin ({{42}^o})}}\]
\[\mu = \dfrac{1}{{0.67}}\]
\[\mu = 1.49\]

So the refractive index of benzene is 1.49.

Note: The refractive index of a liquid varies with temperature and pressure. But relative RI does not. The molar refraction is the specific refraction multiplied by the molecular weight. And as the density increases the refractive index also increases i.e. why refractive index of hot water is high as compared to cold water.