Question

Two prisms of identical geometrical shape are combined with their refracting angles oppositely directed. The materials of the prisms have refractive indices 1.52 and 1.62 for violet light. A violet ray is deviated by 1.0° when passes symmetrically through this combination. What is the angle of the prisms?

Answer 1

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angle of prim will be 10°

Answer 2

The angle of the prisms is $10^{\circ}$

Explanation:

Step 1:

Let ,the angle of the prisms be A

Given, Refracting indices of the prisms for violet light are ,

      $\mu_{1}=1.52$  and   $\mu_{2}=1.62$

Angle of deviation, $\delta=1^{\circ}$

Step 2:

As the prisms are oppositely directed, the angle of deviation is given as

$\delta=\left(\mu_{2}-1\right) A-\left(\mu_{1}-1\right) A$

$\delta=\left(\mu_{2}-\mu_{1}\right) A$

By cross multiplying

$A=\frac{\delta}{\mu_{2}-\mu_{1}}$

Step 3:

Substituting the value of refractive indices and angle of deviation in above equation we get

      $A=\frac{1}{1.62-1.52}$

By solving above equation we get

     $A=10^{\circ}$

So, the angle of prism is $10^{\circ}$