Q.

The X-Y plane be taken as the boundary between two transparent media M1 and M2. M1 in Z0 has a refractive index of 2 and M2 with z<0 has a refractive index of 3. A ray of light travelling in M1 along the direction given by the vector A=43i^33j^5k^ is incident on the plane of separation. The value of difference between the angle of incident in M1 and the angle of refraction in M2 will be ____________ degree

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answer is 15.

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Detailed Solution

A=43i^33j^5k^
Question Image
μ1sini=μ2sinr
As incident vector A makes i angle with normal z-axis & refracted vector R makes r angle with
normal z – axis with help of direction cosine
i=cos1AzA=cos15(43)2+(33)2+52=cos1510i=602sin60=3×sinrr=45
Difference between i & r = 60-45 =15

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