Question

Two identical prisms with slightly different indices are located as shown. Angle q is small. When a laser beam strike one of the prisms perpendicular to the surface, the refracted ray is deviated by a small angle f. Find the difference between the indices of refraction of the prism in term of q&f -

• A. $\frac { \theta } { \phi }$
• B. $\frac { \phi } { \theta }$
• C. $\frac { 2 \phi } { \theta }$
• D. $\frac { 2 \theta } { \phi }$

Answer 1

Answer: (B)

$\frac { \phi } { \theta }$

Answer 2

n₁ sinq = n₂ sinr

n₁q = n₂r for small angles

we can apply Snell's law at the exit vertical plane of the second prism.

n₂ sin (r – q) = sin f

n₂r – n₂q = f

n₁ q = n₂r

$\frac { \mathrm { n } _ { 1 } \mathrm { n } _ { 2 } \theta } { \mathrm { n } _ { 2 } }$ – n₂q = f]

n₁ – n₂ = $\frac { \phi } { \theta }$