Question

A white light is incident at 20⁰ on a material of silicate flint glass slab as shown. µ_voilet = 1.66 and µ_r = 1.6. For what value of d will the separation be 1 mm in red and violet rays.

• A. $\frac { 5 } { 3 }$cm
• B. $\frac { 10 } { 3 }$cm
• C. 5 cm
• D. $\frac { 20 } { 3 }$cm

Answer 1

Answer: (B)

$\frac { 10 } { 3 }$cm

Answer 2

sin r₁ = $\frac { \sin 70 } { 1.66 }$ = $\frac { .9397 } { 1.66 }$ or r₁ = 34⁰30'

sin r₂ = $\frac { \sin 70 } { 1.6 }$ =$\frac { .9397 } { 1.6 }$or r₂ = 36⁰

Using y =

y₁ – y₂ = d

0.1 = d $\left[ \frac { \sin 35 ^ { \circ } 30 ^ { \prime } } { \cos 34 ^ { \circ } 30 ^ { \prime } } - \frac { \sin 34 ^ { \circ } } { \cos 36 ^ { \circ } } \right]$

or 0.1 = d$\left[ \frac { 0.5807 } { 0.8241 } - \frac { 0.5592 } { 0.8090 } \right]$= d[0.71 – 0.68]

or d =$\frac { 0.1 } { 0.03 }$=$\frac { 10 } { 3 }$cm.