The refractive indices of violet and red light are 1.54 and 1.52 respectively. If the angle of prism is 10°, the angular dispersion in degrees is?

Steps to Solve

1. Identify the given values

The refractive indices for violet and red light, and the angle of the prism are given as:

• Refractive index of violet light, $n_v = 1.54$
• Refractive index of red light, $n_r = 1.52$
• Angle of the prism, $A = 10^\circ$

2. Calculate the angle of deviation for violet light

The angle of deviation for a prism is given by the formula: $$ D_v = A(n_v - 1) $$ Substituting the values: $$ D_v = 10^\circ (1.54 - 1) $$ $$ D_v = 10^\circ \times 0.54 $$ $$ D_v = 5.4^\circ $$

3. Calculate the angle of deviation for red light

Similarly, for red light: $$ D_r = A(n_r - 1) $$ Substituting the values: $$ D_r = 10^\circ (1.52 - 1) $$ $$ D_r = 10^\circ \times 0.52 $$ $$ D_r = 5.2^\circ $$

4. Calculate the angular dispersion

Angular dispersion is the difference between the deviations for violet and red light: $$ \text{Angular Dispersion} = D_v - D_r $$ Substituting the values: $$ \text{Angular Dispersion} = 5.4^\circ - 5.2^\circ $$ $$ \text{Angular Dispersion} = 0.2^\circ $$