A ray of light strikes a transparent rectangular slab of refractive index `sqrt(2)` at an angle of incidence of `45^(@)`. The angle betweent the reflected and refracted rays is

Options

A. `75^@`
B. `90^@`
C. `105^@`
D. `120^@`

Answer

C

Explanation

Here , `i = 45^@`
Applying snell.s law at air - glass, surface
`""^amu_g = (sin i)/(sin r.) `
`(mu_g)/(mu_a) = (sin i)/(sin r.)`
`mu_a sin I = mu sin r^2`
`(I sin i)/(sqrt2) = sin r.`
`1/(sqrt2) sin 45^@ = sin r. `
`1/(sqrt2) xx 1/(sqrt2) = sin r.`
`1/2 = sin r.`
`r. = 30^@`
From figure,
`theta + r + r. = 180^@`
(i = r, always (`/_` incidence = `/_`reflection)
`theta = 180^@ - 75^@`
`theta = 105^@`