A parallel beam of light containing two wavelengths, λ1 = 455 nm and λ2 = 642 nm, enters the silicate flint glass of an equilateral prism as shown in (Figure 1).
Figure1 of 1

Part A
At what angles, θ1 and θ2, does each beam leave the prism (give angle with normal to the face)? Use n455nm = 1.64 and n642nm =1.62.
Express your answers using three significant figures separated by a comma.

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:
\[
n \sin(\theta_2) = n_{\text{air}} \sin(i)
\]


A parallel beam of light containing two wavelengths, λ1 = 455 nm and λ2 = 642 nm, enters the silicate flint glass of an equilateral prism as shown in (Figure 1). At what angles, θ1 and θ2, does each beam leave the prism (give angle with normal to the face)? Use n455nm = 1.64 and n642nm =1.62. Express your answers using three significant figures separated by a comma.

Learn how to calculate the exit angles of light beams with wavelengths 455 nm and 642 nm as they pass through a silicate flint glass prism. This problem uses Snell's Law and prism refraction principles to find the exit angles at the second face of the prism. The refractive indices used are n455nm = 1.64 and n642nm = 1.62.

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