In figure, the reflected ray B makes an angle `90^@` with the ray C. If I,`r_1 and r_2` are the angles of incidence, reflection and refraction, respectively. Then, the critical angle of the medium is

Options

A. `sin^-1(tan i)`
B. `sin^-1(cot i)`
C. `r_1`
D. `r_2`

Answer

A

Explanation

`r_1=i and r_2=90^@-r_1=90^@-i`
Now, `mu_Rsini_R=mu_Dsini_D`
or `mu_R/mu_D=sin theta_C=(sini_D)/(sini_R)=sini/(sin(90^@-1))`
or `sin theta_C=sini/cosi=tani`
`rArr theta_C=sin^-1(tani)`