To determine the exit angles $\theta_1$ and $\theta_2$ for each wavelength, we can apply Snell's law at both the entry and exit faces of the prism.

Since the prism is equilateral (60° angle between faces), let's proceed with the calculations in two main steps:

1. Step 1: Calculate the refraction angle inside the prism.
2. Step 2: Determine the exit angle from the prism.

Let’s define the parameters:

• Incident Angle at the first face, $i = 0°$ (assuming it’s normal to the prism's surface).
• Prism Angle $A = 60°$.
• Refractive Indices:
  • For $\lambda_1 = 455 \, \text{nm}$: $n_1 = 1.64$
  • For $\lambda_2 = 642 \, \text{nm}$: $n_2 = 1.62$

Since light is entering normal to the first face, the incident angle is zero, and therefore there’s no initial deviation at entry.

Step 1: Calculate the Angle of Refraction inside the Prism, $r$

Inside the prism, the angle with the normal at the opposite face (after bending) will be influenced by the prism's geometry.

The refraction angle $r$ for each wavelength as light exits the prism can be determined by using the prism formula: $n \sin(\theta_2) = n_{\text{air}} \sin(i)$