Question

From the given data set determine the angular dispersion by the prism and dispersive power of its material foextreme colors ng = 1.62, n = 1.66, 8g = 3.1°.​

Answer 1

Answer:

The angular dispersion is $0.2^\circ$

The dispersive power of the prism is $0.0625$

Explanation:

Angle of deviation for red colour

$\delta_R=3.1^\circ$

Given, the refractive index dor red colour

$\mu_R=1.62$

We know that

$\delta_R=(\mu_R-1)A$

$3.1^\circ=(1.62-1)A$

$\implies A=\frac{3.1^\circ}{0.62}$

$\implies A=5^\circ$

Therefore, the angle of prism is $5^\circ$

The angle of deviation for the violet colour

$\delta_V=(\mu_V-1)A$

$\implies \delta_V=(1.66-1)\times 5^\circ$

$\implies \delta_V=3.3^\circ$

The angle of deviation for the yellod colour (mean angle of deviation)

$\delta_Y=\frac{\delta_R+\delta_V}{2}$

$\implies \delta_Y=\frac{3.1^\circ+3.3^\circ}{2}$

$\implies \delta_Y=3.2^\circ$

The angular dispersion by the prism

$\theta=\delta_V-\delta_R$

$\theta=3.3^\circ-3.1^\circ$

$\theta=0.2^\circ$

The dispersive power of the prism

$\omega=\frac{\theta}{\delta_Y}$

$\implies \omega=\frac{0.2}{3.2}$

$\implies \omega=0.0625$

Hope this helps.