A ray of monochromatic light is incident on a glass prism as shown - Scottish Highers Physics - Question 9 - 2018

The critical angle is defined as the angle of incidence in the denser medium at which light is refracted at an angle of 90° to the normal, resulting in total internal reflection. Beyond this angle, all light is reflected back into the denser medium, and no refraction occurs.

To calculate the critical angle (θc) for the glass, we can use the formula:

$\sin(\theta_c) = \frac{n_2}{n_1}$

Where:

• n1 (refractive index of air) = 1
• n2 (refractive index of glass) = 1.89

Substituting these values:

$\sin(\theta_c) = \frac{1}{1.89}$

Calculating this gives:

$\theta_c = \sin^{-1}(\frac{1}{1.89}) \approx 31.9°$

Therefore, the critical angle is approximately 31.9°.

In completing the diagram:

• The angle of incidence on the second face of the prism can be calculated as 60° (the angle inside the prism).
• Applying the rules of total internal reflection, the ray exiting into the air will have angles labeled: 38° for the angle of refraction entering air and 22° and 45° for the angles made with the normal on exiting.

The required angles should be clearly marked on the diagram.

One key difference in the spectrum produced by the second prism with a lower refractive index is that it will show less deviation in the spectrum position. This is due to the lower refractive index causing a smaller bending of light rays as they pass through, resulting in a wider spread of the spectrum and less dispersion compared to the first prism.