Question

A ray of light incident in air strikes a rectangular glass block of refractive index 1.50, at an angle of incidence of 45°. Calculate the angle of refraction in the glass.​

Answer 1

Approximately
`28^(\circ)`.

Step-by-step explanation:

The refractive index of the air
`n_{\text{air}}` is approximately
`1.00`.

Let
`n_\text{glass}` denote the refractive index of the glass block, and let
`\theta _{\text{glass}}` denote the angle of refraction in the glass. Let
`\theta_\text{air}` denote the angle at which the light enters the glass block from the air.

By Snell's Law:

`n_{\text{glass}} \, \sin(\theta_{\text{glass}}) = n_{\text{air}} \, \sin(\theta_{\text{air}})`.

Rearrange the Snell's Law equation to obtain:

`\begin{aligned} \sin(\theta_{\text{glass}}) &= \frac{n_{\text{air}} \, \sin(\theta_{\text{air}})}{n_{\text{glass}}} \\ &= ((1.00)\, (\sin(45^(\circ))))/(1.50) \\ &\approx 0.471\end{aligned}`.

Hence:

`\begin{aligned} \theta_{\text{glass}} &= \arcsin (0.471) \approx 28^(\circ)\end{aligned}`.

In other words, the angle of refraction in the glass would be approximately
`28^(\circ)`.