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The x-z plane separates two media A and ...

The x-z plane separates two media A and B of refractive indices `mu_(1) = 1.5` and `mu_(2) = 2`. A ray of light travels from A to B. Its directions in the two media are given by unit vectors `u_(1) = a hat(i)+b hat(j)` and `u_(2) = c hat(i) +a hat(j)`. Then

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so `sin i=a/sqrt(a^2+b^2)`
and `tanr = c/d , sin r= c/sqrt(c^2+d^2)`
`mu_1 sin i =mu_2 sin r (3/2) (a/sqrt(a^2+b^2))=2 (c/sqrt(a^2+b^2))`
But as `a hati+b hat j and c hati +d hat j` are unit vectors so
`sqrt(a^2+b^2)=sqrt(c^2+d^2)=1`
Hence `3/2a=2c, so a/c=4/3`
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