Question

A prism of dispersive power $0.021$ and refractive index $1.52$ to form an achromatic combination with the second prism of refracting angle 4.2${}^{\circ }$ and dispersive power $0.036$ having refractive index $1.65$. The resultant deviation is:

• A. ${1.25}^{\circ }$
• B. ${1.95}^{\circ }$
• C. ${2.50}^{\circ }$
• D. ${5.20}^{\circ }$

Answer 1

The correct option is B ${1.95}^{\circ }$

For achromatic combination,

$({\mu }_{v,1}-{\mu }_{r,1})\times A_1=({\mu }_{v,2}-{\mu }_{r,2})\times A_2$

Also dispersive power $\omega =({\mu }_v-{\mu }_r)/({\mu }_y-1)$

So ${\omega }_1\times ({\mu }_{y,1}-1)\times A_1={\omega }_2\times ({\mu }_{y,2}-1)\times A_2$

=> $0.021\times 0.52\times A_1=0.036\times 0.65\times 4.2$

=> $A_1=9^{\circ }$

Resultant deviation is $|({\mu }_1-1)\times A_1-({\mu }_2-1)\times A_2|$

$=|(1.52-1)\times 9-(1.65-1)\times 4.2|$

$={1.95}^o$