Question

The dispersive power 0.021 and refractive index 1.52 to form an achromatic combination with a prism of angle $4.2$ and dispersive power 0.036 having refractive index 1.65. the resultant deviation

• A. $1.25$
• B. $0.91$
• C. $2.5$
• D. $5.2$

Answer 1

The correct option is B $0.91$

$\begin{array}{c}{A}_1=4\cdot 2\\ {\omega }_1=0.021\\ {\mu }_1=1.52\\ A_2=?\\ {\omega }_2=0.036\\ {\mu }_2=1.65\end{array}$

$\begin{array}{c}\text{W = dispersive power}\\ d=\text{deviation}\\ A=\text{angle of}\text{prism}\\ \mu =\text{refractive index.}\end{array}$

$\begin{array}{c}{\omega }_1{\delta }_1+w_2{\delta }_2=0\\ \omega A(\mu -1)+{\omega }_2{A}_2({\mu }_2-1)=0\\ 0.021\times 4\cdot 2\left(0.52\right)+0.036A_2\left(0.65\right)=0\\ A_2=-\frac{0.021\times 4.2\times 0.52}{0.036\times 0.65}\\ =-1.96\end{array}$

$\begin{array}{cc}\text{Resultant}\delta =& ({\mu }_1-1)A_1+({\mu }_2-1)A_2\\ & =(1.52-1)4.2+(1.65-1)(-1.96)\\ & =0.91\end{array}$