A ray of blue light is incident on a triangular glass prism as shown - Scottish Highers Physics - Question 11 - 2023

Using the interior angles of the triangle, we have:

$B = 180 - 60 - A$ Substituting the value of A:

$B = 180 - 60 - 84 = 36.0 \text{ degrees}$

The critical angle is defined as the angle of incidence at which light is refracted along the boundary between two different media, resulting in an angle of refraction of 90 degrees. Beyond this angle, total internal reflection occurs.

The critical angle can be calculated using Snell's Law:

$n_1 \sin(\theta_c) = n_2 \sin(90)$

Where:

• $n_1 = 1.53$ (refractive index of glass)
• $n_2 = 1.0$ (refractive index of air)

Substituting:

$1.53 \sin(\theta_c) = 1.0 \times 1$

Thus,

$\sin(\theta_c) = \frac{1.0}{1.53}$

Calculating:

$\theta_c = \sin^{-1}(0.653) \approx 40.8 \text{ degrees}$

The ray should be drawn emerging from the glass to the air at an angle greater than angle B. Since we've determined angle B to be 36.0 degrees, the angle of refraction can be calculated from the critical angle and marked on the diagram:

• Draw the emergent ray at an angle of approximately 68.3 degrees to the normal (which can be obtained from previously calculated values).