Question

A glass prism deviates the red and blue rays through ${10}^{\circ }$ and ${12}^{\circ }$ respectively. A second prism of equal angle deviates them through $8^{\circ }$ and ${10}^{\circ }$ respectively. Their dispersive powers are in the ratio

• A. 11: 9
• B. 9 :11
• C. 3 : 2
• D. 1 : 1

Answer 1

The correct option is B 9 :11

$w=\frac{Dv-Dr}{D};D=\frac{Dv+Dr}{2}{D}_1=\frac{12+10}{2}\frac{W_1}{W_2}=\frac{{\left[\frac{Dv-Dr}{D}\right]}_1}{{\left[\frac{Dv-Dr}{D}\right]}_2}=11D_2=\frac{10+8}{2}=\frac{\left(\frac{12-10}{11}\right)}{\left(\frac{10-8}{9}\right)}=9=\frac{2\times 9}{11\times 2}{W}_1=W_{2}9:11$