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Let the x-z plane be the boundary betwee...

Let the x-z plane be the boundary between two transparent media. Medium 1 in `zge0` has a refractive index of `sqrt2` and medium 2 with `zlt0` has a refractive index of `sqrt3`. A ray of light in medium 1 given by the vector `vecA=6sqrt3hati+8sqrt3hatj-10hatk` is incident on the plane of separation. The angle of refraction in medium 2 is:

A

`30^(@)`

B

`45^(@)`

C

`60^(@)`

D

`75^(@)`

Text Solution

Verified by Experts

The correct Answer is:
B
`cos (pi - i) = (( 6 sqrt(3) hat(i) + 8 sqrt(3) hat(j) - 10 hat(k)).hat(k))/(sqrt((6 sqrt(3))^(2)+ 8(8 sqrt(3))^(2)+ (10)^(2)))`
`= (-10)/( sqrt(400)) = (-10)/(20)`
`rArr cos (pi - i) = - (1)/(2) rArr pi - i = 120^(@) rArr i = 60^(@)`
Now, Snell.s law,
`n_(1) sin i = n_(2) sin r `
`rArr sqrt(2) sin 60^(@) = sqrt(3) sin r `

` rArr sin r = (sqrt(2) xx sqrt(3))/( 2 xx sqrt(3)) = (1)/( sqrt(2))`
`rArr r = 45^(@)`
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