Question

The refractive indices of violet and red light are 1.54 and 1.52 respectively. If the angle of prism is 10?, then the angular dispersion is [MP PMT 1990]
A) 0.02 B) 0.2 C) 3.06 D) 30.6

Answer 1

OptionB) 0.2
10(1.54-1.52)=0.2

Answer 2

Answer:

The angular dispersion is 0.2.

Option B is correct.

Explanation:

Given that,

Angle of prism = 10°

The refractive indices of violet and red light are

$\mu_{v}=1.54$

$\mu_{r}=1.52$

The formula of deviation for violet light

$\delta_{v}=(\mu_{v}-1)A$....(I)

The formula of deviation for red light

$\delta_{r}=(\mu_{r}-1)A$.....(II)

The angular dispersion is angle between of two colors of light.

$\delta_{v}-\delta_{r}=(\mu_{v}-1)A-(\mu_{r}-1)A$

$\delta_{v}-\delta_{r}={(\mu_{v}-1)-(\mu_{r}-1)}A$

$\delta_{v}-\delta_{r}={1.54-1)-(1.52-1)}\times10$

$\delta_{v}-\delta_{r}={(1.54-1.52)}\times10$

$\delta_{v}-\delta_{r}=0.2$

Hence, The angular dispersion is 0.2.