Question

Dispersion without deviation is produced by two thin (small angled) prisms which are combined together. One prism has angle $ 5^{\circ} $ and refractive index $ 1.56 $ . If the other prism has refractive index $ 1.7 $ , what is its angle ?

• A. $ 3^{\circ} $
• B. $ 4^{\circ} $
• C. $ 5^{\circ} $
• D. $ 6^{\circ} $

Answer 1

Answer: (B)

Dispersion without deviation by combining two prisms of angles $A_{1}$ and $A_{2}$ with refractive indices $n_{1}$ and $n_{2}$ is given by
$(n_{1}-1)A_{1}=(n_{2}-1)A_{2} \dots(i)$
Here $n_{1}=1.56, A_{1}=5^{\circ}, n_{2}=1.7$
From equation (i),
$\Rightarrow (1.56-1)\times 5$
$=(1.7-1) \times A_{2} ; A_{2} =4^{\circ}$