Question

A thin prism having refracting angle ${10}^o$ is made of glass of refractive index $1.42$. This prism is combined with another thin prism of glass of refractive index $1.7$. This combination produces dispersion without deviation. The refracting angle of second prism should be

• A. ${10}^o$
• B. $4^o$
• C. $6^o$
• D. $8^o$

Answer 1

The correct option is C $6^o$

Dispersion without deviation this means that ray which is entering and the ray which is going out both are parallel,
As given,
$A_1=\text{refracting angle of first prism}={10}^o$, ${\mu }_1=1.42,{\mu }_2=1.7$
$A_2=\text{refracting angle of second prism}$
As, $\delta =(\mu -1)A$
So, ${\delta }_{\text{Total}}={\delta }_1-{\delta }_2=0$
where $\delta$ is the daviation and in this case total deviation is zero.
${\delta }_1={\delta }_2$
$A_2({\mu }_2-1)=A_1({\mu }_1-1)$
$A_2\left(0.7\right)=10\left(0.42\right)$
$A_2=6^0$