Q9DQ - University Physics with Modern Physics

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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.

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

Step 2: 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.