Answer to Question #96919 in Optics for Halima

Question

Two thin(small angled)prism are combined to produce dispersion without deviation. One prism has angle 5A^° and refractive index 1.56.if the other prism has refractive index 1.7,what is its angle?

Answer 1

Angle of Prism

We need to find the Angle of the second prism

Solution:

We know the formula to find the deviation produced by a Prism, that is

$$d = (\mu - 1) A$$

In this,

d = Deviation produced by the Prism

$\mu =$ Refractive index of the Prism

A = Angle of the Prism

Here, We are working on two prisms.

$d_1 =$ Deviation produced by the first Prism

$d_2 =$ Deviation produced by the second Prism

$A_1 =$ Angle of the first Prism = $5^{o}$

$A_2 =$ Angle of the second Prism

$\mu_1 =$  Refractive index of the first Prism = 1.56

$\mu_2 =$ Refractive index of the second  Prism = 1.7

Without deviation, means,

$$d_1 = d_2 = 0$$

Th equations

$$d_1 = (\mu_1 - 1) A_1$$

$$d_2 = (\mu_2 - 1) A_2$$

$$(\mu_1 - 1) A_1 =(\mu_2 - 1) A_2$$

PLug the values in this,

$$(1.56 - 1) 5 = (1.7 - 1) A_2$$

$$A_2 = \frac {0.56 \times 5} {0.7} = 4^{o}$$

Answer: Angle of the second Prism

$$A_2 = 4^{o}$$