The figure below shows an initial incident light ray that is refracted twice, fi

Question

The figure below shows an initial incident light ray that is refracted twice, first by going through a horizontal interface between two materials with indices of refraction...

Problem #1 (20 points) The figure below shows an initial incident light ray that is refracted twice, first by going through a horizontal interface between two materials with indices of refraction n 1.23 and n2 1.44 and second by going through a vertical interface between two materials with indices of refraction n2 1.44 and n 1.66 Initial Incident Ray n2 n3 Final Refracted Ray The final refracted ray is parallel to the initial incident ray If the final refracted ray emerges so that it is parallel to the initial incident ray, determine the value of the angle ?- Hint: Recall that sin(900-8) cos(0), cos(90-0)in(0) and sin2(0)cos () 1

Explanation / Answer

For the final and initial ray to be parallel,

?1+?4=900

So,

Applying snell's law ,

nsin?= constant.

So,

n1sin?1=n3sin?4

n1sin?1=n3sin(90-?1)

n1sin?1=n3cos?1

tan?1=1.66/1.23

tan?1=1.3495

?1=53.462890

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