Name: Dual Nature of Radiation
Uploaded: 2019-07-19
Duration: 3 min 36 s
Description: What is the nature of light? Is it a wave or a particle? The answer is light has a dual nature. Light can be treated as a particle as well as a wave.

Question

Define angular dispersion for a prism. Obtain its expression for a thin prism. Relate it with the refractive indices of the material of the prism for corresponding colours.

Accepted Answer

The angular dispersion is defined as the angle between the two extreme colours of light. The dispersive power of a prism is defined as the ratio of angular dispersion to the deviation of mean colour.

Thin prism is the triangular prism made of transparent material (glass) of apex angle very small does not exceed $10^{\circ}$ and always set at the position of minimum deviation.

Consider a thin prism of angle $A$ and refractive index $n$ . Let $i_{1}$ be the angle of incidence, $r_{1}$ be the angle of refraction at the first face, $r_{2}$ be the angle of incidence at the second face and $i_{2}$ be the angle of emergence. If $d$ is the angle of deviation.

$d = (i_{1} + i_{2}) - A$ .......................(1)

$A = r_{1} + r_{2}$ ........................(2)

For a thin prism, when the angle of incidence $i_{1}$ is small, the angles $r_{1}, r_{2}, i_{2}$ are small.

$n = \frac{\sin i_{1}}{\sin r_{1}} \approx \frac{i_{1}}{r_{1}} n = \frac{\sin i_{2}}{\sin r_{2}} \approx \frac{i_{2}}{r_{2}}$

From equation(1).

$d = (n r_{1} + n r_{2}) - A = n (r_{1} + r_{2}) - A = n A - A d = A (n - 1)$

Define angular dispersion for a prism. Obtain its expression for a thin prism. Relate it with the refractive indices of the material of the prism for corresponding colours.

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