Question

Consider that a ray of light is travelling from glass to water. The refractive index of water is 1.30 (i e n . ., 1.30 w = ) and refractive index of glass is 1.70 (i e n . ., 1.70 g = ). Again, remind yourself that light is incident from glass to water. At the glass-water interface the light suffers total internal reflection (TIR). Find the condition for total internal reflection

Answer 1

Answer:

$\theta_i=49.88^{\circ}$

Explanation:

Total internal reflection can happen when light goes from a medium with higher refractive index (in this case, glass) to a medium with lower refractive index (in this case, water).

Snell's Law tells us that $n_isin\theta_i=n_rsin\theta_r$, where the i stands for incident (in this case, glass) and the r for refracted (in this case, water). We want to know when $\theta_r=90^{\circ}$, that is, when $n_isin\theta_i=n_r$, and this happens when the incident angle is:

$\theta_i=arcsin(\frac{n_r}{n_i})$

Which for our values means:

$\theta_i=arcsin(\frac{1.3}{1.7})=arcsin(0.76470588235)=49.88^{\circ}$