A ray of light from a denser medium strikes a rarer medium at angle of incidence `i`. The refrected and the refracted rays make an angle of `90^@` with each other. The angles of reflection and refraction are r and `r^'` respectively. The critical angle is
(i) `sin^-1(tanr)`
(ii) `sin^-1(tani)`
(iii) `sin^-1(tanr)`
(iv) `tan^-1(tani)`

Options

A. (i), (ii)
B. (ii), (iii)
C. (i), (iii)
D. (ii), (iv)

Answer

A

Explanation

`r+r^'=90^@impliesr^'=90-r, i=r`
`mu_1sini=mu_2sinr^'=mu_2sin(90-r)`
`mu_1sinr=mu_2cosr`
`mu_2/mu_1=tanr=tani`
Critical angle for denser to rarer medium
`mu_1sinC=mu_2sin90^@`
`sinC=(mu_2)/(mu_1)=tanr=tani`
`C=sin^-1(tanr)=sin^-1(tani)`