Compare the dispersive powers of two prisms if one of them deviates the blue and red rays through 10° and 6° respectively and the second prism through 8° and 4.5°

Question

Compare the dispersive powers of two prisms if one of them deviates the blue and red rays through 10° and 6° respectively and the second prism through 8° and 4.5° (A) 0.69 (B) 0.79 (C) 0.89 (D) 0.99

Tardigrade Admin · Accepted Answer

Dispersive power =(δv-δr/δy) δy=(δv+δr/2) w1=(10-6/8)=(1/2) w2=(8-4.5/6.25)=(3.5/6.25) (w1/w2) ≈ 0.89

Q. Compare the dispersive powers of two prisms if one of them deviates the blue and red rays through $1 0^{\circ}$ and $6^{\circ}$ respectively and the second prism through $8^{\circ}$ and $4. 5^{\circ}$

$0.69$

$0.79$

$0.89$

$0.99$

Dispersive power $= \frac{δ _{v} - δ _{r}}{δ _{y}}$
$δ_{y} = \frac{δ _{v} + δ _{r}}{2}$
$w_{1} = \frac{10 - 6}{8} = \frac{1}{2}$
$w_{2} = \frac{8 - 4.5}{6.25} = \frac{3.5}{6.25}$
$\frac{w _{1}}{w _{2}} \approx 0.89$

Q. Compare the dispersive powers of two prisms if one of them deviates the blue and red rays through 10∘ and 6∘ respectively and the second prism through 8∘ and 4.5∘

0.69

0.79

0.89

0.99