Question

which of thereflecred ray if liquid taken is benzene​

Answer 1

The refractive index,  of benzene with respect to air is 1.8.

[math]\Rightarrow \qquad[/math] The refractive index of air with respect to benzene is [math]\frac{1}{\mu}=\frac{1}{1.8}.[/math]

Consider a ray of light travelling from the medium benzene to the medium air. Let the angle of incidence be [math]i[/math] and the angle of refraction be r.

At the critical angle, when total internal reflection just starts, [math]r=90^o[/math] and [math]i=i_c.[/math]

[math]\Rightarrow \qquad \frac{\sin i_c}{\sin r}=\frac{\sin i_c}{\sin 90^o} = \frac{1}{\mu}=\frac{1}{1.8}.[/math]

[math]\Rightarrow \qquad \sin i_c=\frac{1}{1.8}.[/math]

[math]\Rightarrow \qquad i_c = \arcsin \left(\frac{1}{1.8}\right)=33.74899^o.[/math]

[math]\Rightarrow \qquad[/math] The critical angle is [math]33.74899^o.[/math]