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 a refractive index greater than the surrounding medium (typically air), it bends towards the normal at the first interface (at angle of incidence \(i\)). It then passes through the prism and bends away from the normal at the second interface (at angle of exit \(e\)). The prism's apex angle is denoted by \(A\).

Step 2: Derive the formula for the angle of deviation (\(\delta\)). The angle of deviation (\(\delta\)) is the extent to which the light ray's direction changes after traversing the prism. This angle can be related to the angle of incidence (\(i\)), the angle of exit (\(e\)), and the prism's apex angle (\(A\)) using the formula: \[ \delta = i + e - A \] This equation is derived from the principle that the total deviation equals the sum of the angles of incidence and emergence minus the prism's apex angle. 

Step 3: Graph the variation of \(\delta\) with \(i\). The relationship between \(\delta\) and \(i\) is non-linear. Generally, \(\delta\) decreases as \(i\) increases, reaching a minimum value (the condition of minimum deviation), and then begins to increase. The resulting graph of \(\delta\) versus \(i\) exhibits a "U" shape, signifying that minimum deviation occurs when the light ray passes symmetrically through the prism.