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A ray of light moving along the vector ...

A ray of light moving along the vector (`-i-2j`)undergoes refraction at an interface two media, which is the x-z plane. The refractive index for `ygt0` is `2` and below it is `sqrt(5)//2`.the unit vector along which the refracted ray moves is:

A

`(-3hati-5hatj)/(sqrt(34))`

B

`(-(4hati-5hatj))/(5)`

C

`(-3hati-4hatj)/(5)`

D

`(4hati-3hatj)/(5)`

Text Solution

Verified by Experts

The correct Answer is:
D
`-(hati-2hatj).hatj=|hati-2hatj||hatj|cos theta rArr cos theta = (2)/(sqrt(5))`
`:. sin theta = (1)/(sqrt(5))`
Using Snell's law at the interface
`2 xx (1)/(sqrt(5)) = (sqrt(5))/(2) sin beta`
` rArr sin beta = 4/5 :. cos beta = 3/5`
So, `hatr = 4/5 hati-3/5hatj`
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