A ray of light is incident on liquid surface such that reflected and refracted ray are perpendicular to each other. If refractive index is 1.4, find angle of incident.

Options

A. `54.5^@`
B. `55.4^@`
C. `5.45^@`
D. `5.54^@`

Answer

A, D

Explanation

From figure,
`theta_1+90^@+theta_2=180^@`
`therefore theta_2=90^@-theta_1`
Now,`n_1sin theta_1=n_2sin theta_2=n^2sin(90^@-theta_1)`
`n_1=1,n_2=1.4,theta_1=?`
`therefore (1)sintheta_1=1.4cos theta_1`
`therefore (sin theta_1)/(cos theta_1)=tantheta_1=1.4`
`therefore theta_1=tan^(-1)(1.4)=54.5^@`