Question

A thin prism deviates blue and red rays through 10${}^{\circ }$ and 6${}^{\circ }$respectively. Another prism deviates same colours through 8${}^{\circ }$ and 4.5${}^{\circ }$ respectively.The ratio of dispersive powers of the prisms is :

• A. 5:4
• B. 4:5
• C. 25:28
• D. 5:28

Answer 1

Answer: (C)

25:28

For a thin prism,

Dispersive power, $w=({\delta }_v-{\delta }_r)/{\delta }_y$

Also, ${\delta }_y=({\delta }_v+{\delta }_r)/2$

Ratio of dispersive power,

$w_1:w_2=\left[\right(10-6)\ast 2/(10+6\left)\right]:\left[\right(8-4.5)\ast 2)/(8+4.5)]$

=> $w_1:w_2=25:28$