Question

A ray of light is incident on a medium of refractive index ` sqrt(2)` at an angle of incidence of `45^(@)`. The ratio of the width of the incident beam in air to that of the refracted beam in the medium is
A. `(3//2)^(1//2)`
B. `(2//3)^(1//2)`
C. `3//2`
D. `2//3`

Answer 1

Correct Answer - B

From the figure ,`("Width of the incident beam")/("Width of the refracted beam ")=(AB)/(CD)`
`:. (cos i)/(cos r)=(AB)/(AC) xx (AC)/(CD)=(AB)/(CD)`
But `n=(sin i)/(sin r) :. sqrt(2)=(sin 45^(@))/(sin r)=(1)/(sqrt(2) sinr )`
`:. sin r=(1)/(sqrt2 xx sqrt(2))=(1)/(2) :. r=30^(@)`
`:. ( cos i)/(cos r)=(cos 45^@)/( cos 30^(@))`
`=((1)/(sqrt(2)))/((sqrt(3))/(2))=(1)/(2) xx (2)/(sqrt(3))=((2)/(3))^(1//2)`