Question

Find the angle of incidence for which angle of deviation from a liquid drop is minimum in a primary rainbow

• A. 30⁰
• B. 40⁰
• C. 50⁰
• D. 60⁰

Answer 1

Answer: (D)

60⁰

Answer 2

sin i = µ sin r … (1)

differentiating eq. (1) cos i di = µ cos r dr

or $\frac { \mathrm { dr } } { \mathrm { di } }$ = $\frac { \cos i } { \mu \cos r }$ = $\frac { 1 } { 2 }$

or 2 cos i = µ cos r

or 4 cos² i = µ² cos² r = µ² (1 – sin² r)

or 4 cos² i = µ² $\left( 1 - \frac { \sin ^ { 2 } \mathrm { i } } { \mu ^ { 2 } } \right)$ = µ² – (1 – cos² i)

or 3 cos² i = µ² – 1

or cos i = $\sqrt { \frac { \mu ^ { 2 } - 1 } { 3 } }$ =$\sqrt { \frac { 7 } { 27 } }$

or cos i =$\sqrt { .26 }$= .5

or i = 60⁰.