Question

A prism of a certain angle deviates the red and blue rays by $8^o$ and ${12}^o$ respectively. Another prism of the same angle deviates the red and blue rays by ${10}^o$ and ${14}^o$ respectively. The prisms are small angled and made of different materials. Dispersive powers of the materials of the prisms are in the ratio :

• A. $5:6$
• B. $9:11$
• C. $6:5$
• D. $11:9$

Answer 1

Answer: (C)

$6:5$

The formula for dispersive power is given as,

$W=\frac{d_b-d_r}{d_{avg}}$

Hence the dispersive power for prism $1$:

$W_1=\frac{12-8}{\left(12+8\right)/2}=\frac{4}{10}=\frac{2}{5}$

The dispersive power for prism $2$:

$W_2=\frac{14-10}{\left(14+10\right)/2}=\frac{4}{12}=\frac{1}{3}$

$\therefore \frac{W_1}{W_2}=\frac{2}{5}\times 3=\frac{6}{5}$

Hence the correct answer is option (C).