Question

A ray of light in air strikes a glass surface. Is there a range of angles for which total internal reflection occurs? Explain.

Short answer

No, there is no range of angles for which total internal reflection occurs.

Step-by-step solution

Definition of Snell’s Law

Snell's law states that, for a given pair of media, the ratio of the sines of the angle of incidence${\mathit{\theta }}_{\mathbf{1}}$ and angle of refraction${\mathit{\theta }}_2$ is equal to the ratio of the refractive indices$\frac{{\mathbf{n}}_{\mathbf{2}}}{{\mathbf{n}}_{\mathbf{1}}}$ of the two media.

$\frac{\mathbf{s}\mathbf{i}\mathbf{n}{\mathbf{\theta }}_{\mathbf{1}}}{\mathbf{s}\mathbf{i}\mathbf{n}{\mathbf{\theta }}_{\mathbf{2}}}\mathbf{=}\frac{{\mathbf{n}}_{\mathbf{2}}}{{\mathbf{n}}_{\mathbf{1}}}$

Determine if range of angles exist

According to Snell’s Law,

$n_1\sin {\theta }_1=n_2\sin {\theta }_2$

where index l designates the air and index 2 designates the glass. For the angle of Refraction, we get

$\sin {\theta }_2=\frac{n_1}{n_2}\sin {\theta }_1$

Total internal reflection occurs when${\theta }_2=90°$ i.e. when$\sin {\theta }_2=1$ . Since$sin{\theta }_1\le 1$ and$n_1<n_2$ we conclude that$\sin {\theta }_2<1$ which means that the total internal reflection is impossible.

Hence, there is no range of angles for which total internal reflection occurs.