Question

An equilateral glass prism is made of a material of refractive index $1.5$. Find its angle of minimum deviation.

• A. $\delta ={37}^0{50}^{\prime }$
• B. $\delta ={47}^0{10}^{\prime }$
• C. $\delta ={37}^0{10}^{\prime }$
• D. $\delta ={34}^0{10}^{\prime }$

Answer 1

The correct option is C $\delta ={37}^0{10}^{\prime }$

$A={60}^0;\mu =1.5;\delta =?$
Substituting in
$\mu =\frac{sin\frac{A+\delta }{2}}{sin\frac{A}{2}};$
$1.5=\frac{sin\left(\frac{{60}^0+\delta }{2}\right)}{sin\left(\frac{{60}^0}{2}\right)}$
$1.5sin{30}^0=sin\left(\frac{{60}^0+\delta }{2}\right)$
$sin\left(\frac{{60}^0+\delta }{2}\right)=1.5\times 0.5000=0.7500$
$\frac{{60}^0+\delta }{2}={48}^0{35}^{\prime }$; ${60}^0+\delta ={97}^0{10}^0$
$\Rightarrow \delta ={37}^0{10}^{\prime }$