Question

a) What is the ratio of the speed of red light to violet light in a diamond? b) What is this ratio in polystyrene? c) Which is more dispersive? (Refractive index of diamond is 2.41 for red light and 2.458 for violet light, and the refractive index of polystyrene is 1.488 for red light and 1.506 for violet light.)

Answer 1

Answer:

(a). The ratio of the speed of red light to violet light in a diamond is 1.019.

(b). The ratio of the speed of red light to violet light in a polystyrene is 1.015.

(c). Polystyrene is more dispersive.

Explanation:

Given that,

Refractive index of diamond

For red light = 2.41

For violet light = 2.458

Refractive index of polystyrene

For red light = 1.488

For violet light = 1.506

(a). We need to calculate the speed of red light in diamond

Using formula of speed

$v=\dfrac{c}{n}$

Where, c = speed of light

v = speed of light

n = refractive index

Put the value into the formula

$v=\dfrac{3\times10^{8}}{2.41}$

$v=1.244\times10^{8}\ m/s$

We need to calculate the speed of violet light in diamond

$v'=\dfrac{3\times10^{8}}{2.458}$

$v'=1.220\times10^{8}\ m/s$

We need to calculate the ratio of the speed of red light to violet light in a diamond

$\dfrac{v}{v'}=\dfrac{1.244\times10^{8}}{1.220\times10^{8}}$

$\dfrac{v}{v'}=\dfrac{311}{305}$

$\dfrac{v}{v'}=1.019$

The ratio of the speed of red light to violet light in a diamond is 1.019.

(b). We need to calculate the speed of red light in polystyrene

Using formula of speed

$v=\dfrac{3\times10^{8}}{1.488}$

$v=2.02\times10^{8}\ m/s$

We need to calculate the speed of violet light in polystyrene

Using formula of speed

$v'=\dfrac{3\times10^{8}}{1.506}$

$v'=1.99\times10^{8}\ m/s$

We need to calculate the ratio of the speed of red light to violet light in a polystyrene

$\dfrac{v}{v'}=\dfrac{2.02\times10^{8}}{1.99\times10^{8}}$

$\dfrac{v}{v'}=1.015$

The  ratio of the speed of red light to violet light in a polystyrene is 1.015.

(c). We need to calculate the dispersive power for diamond

Using formula of dispersion

$\omega=\dfrac{\mu_{v}-\mu_{r}}{\mu_{y}-1}$

Put the value into the formula

$\omega=\dfrac{2.458-2.41}{2.417-1}$

$\omega=0.0338$

We need to calculate the dispersive power for polystyrene

$\omega=\dfrac{1.506-1.488}{1.492-1}$

$\omega=0.0365$

Polystyrene is more dispersive.

Hence, This is the required solution.