Question

Trace the path of a ray of light showing refraction through a triangular prism and hence obtain an expression for the angle of deviation (\(\delta\)) in terms of \(A\), \(i\), and \(e\), where symbols have their usual meanings. Draw a graph showing the variation of the angle of deviation with the angle of incidence.

Hint:

When plotting the graph of angle of deviation versus angle of incidence, note that the minimum angle of deviation occurs when the light path through the prism is symmetrical. This principle is used in optical instruments to achieve precise angular measurements.

Answer 1

Step 1: Trace the path of the ray of light through the prism. When a ray of light enters a prism with refractive index greater than that of the surrounding medium (typically air), it bends towards the normal at the first interface (at angle of incidence \(i\)), passes through the prism, and bends away from the normal at the second interface (at angle of exit \(e\)). The prism has an apex angle \(A\). 

Step 2: Derive the formula for the angle of deviation (\(\delta\)). The angle of deviation (\(\delta\)) is the angle by which the light ray deviates from its original direction after passing through the prism. It can be expressed in terms of the angle of incidence (\(i\)), the angle of exit (\(e\)), and the prism's apex angle (\(A\)) as follows: \[ \delta = i + e - A \] This relationship arises because the external deviation is equal to the sum of the angles of incidence and emergence minus the angle of the prism. 

Step 3: Graph the variation of \(\delta\) with \(i\). The relationship between \(\delta\) and \(i\) is typically non-linear, showing that \(\delta\) decreases with an increase in \(i\) up to a minimum value (at the minimum deviation condition) and then increases. The graph of \(\delta\) versus \(i\) will have a "U" shape, indicating the minimum deviation occurs when the light ray passes symmetrically through the prism.