Question

A certain material has refractive indices 1.56, 1.60 and 1.68 rfor red, yellow and violet lightespectively. (a) Calculate the dispersive power. (b) Find the angular dispersion produced by a thin prism of angle 6° made of this material.

Answer 1

(a) $\omega=0.2$, (b) $angular dispersion 0.72^{\circ}$.

Explanation:

(a) Dispersive power  $\omega=\frac{\mu_{v}-\mu_{r}}{\mu_{y}-1}$

where    $\mu_{v}$=refractive index for violet light

$\mu_{r}$=refractive index for red light

$\mu_{y}$=refractive index for yellow light

$\mu_{v}=1.68$

$\mu_{r}=1.56$

$\mu_{y}=1.60$

By putting the value in dispersive power equation we get

w  $=\frac{1.68-1.56}{1.60-1}$

$\omega=0.2$

(b) angular dispersion $\left(\mu_{v}-\mu_{r}\right) \times \theta$

$=(1.68-1.56) \times 6$                           (angle of prism=$6^{0}$)

=0.720

Answer 2

$\huge{\boxed{\mathcal\pink{\fcolorbox{red}{yellow}{Answer}}}}$

$(a) \omega \: = 0.2 \\ (b) \: angle \: of\: dispersion= 0.072$