Question

A thin prism is made of a material having refractive indices 1.61 and 1.65 for red and violet light. The dispersive power of the material is 0.07. It is found that a beam of yellow light passing through the prism suffers a minimum deviation of 4.0° in favourable conditions. Calculate the angle of the prism.

Answer 1

The angle of prism is $A=7^{\circ}$

Explanation:

Step 1:

Given ,

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

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

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

$\mu_{v}=$ 1.65

$\mu_{r}=$ 1.61

$\omega=$  0.07

δ = 4°

By using the dispersive power equation, $\omega=\frac{\mu_{v}-\mu_{r}}{\mu_{y}-1}$

Step 1 :-    $p \cdot 07=\frac{1.65-1.61}{\mu_{y}-1}$

Step 2 :-    $\mu_{y}-1=\frac{4}{7}$

Also angel of minimum deviation is given as  $\delta=(\mu-1) A$

For minimum deviation $\mu=\mu_{y}$

$A=\frac{\delta}{\mu_{y}-1}$

By substituting the value of δ and $\mu_y$ in above equation we get angle of prism  $A=7^{\circ}$