The maximum value of index of refraction of a material of a prism which allows the passage of light through it when the refracting angle of prism is A is

Options

A. `sqrt(1+sin(A/2))`
B. `sqrt(1+cos(A/2))`
C. `sqrt(1+tan^(2)(A/2))`
D. `sqrt(1+cot^(2)(A/2))`

Explanation

(d) Situation is shown in figure.
`r_(1)=C,r_(2)=C`
`r_(1)+r_(2)=A`
`:.2C=A,C=A/2`
`:.mu=1/(sin C)=1/(sin (A/2))`
`=(sqrt(sin^(2)(A/2)+cos^(2)(A/2)))/(sin (A/2))=sqrt(1+cot^(2)(A/2))`