A beam of light both reflects and refracts at the surface between air and glass,

Question

A beam of light both reflects and refracts at the surface between air and glass, as shown in the figure below. If the index of refraction of the glass is ng, find the angle of incidence, ?1, in the air that would result in the reflected ray and the refracted ray being perpendicular to each other. Hint: Remember the identity sin(90° - ?) = cos ?. (Use any variable or symbol stated above as necessary.)

What is ?1 equal to? Please explain how you solved it. Thanks

http://www.webassign.net/sercp9/22-p-025.gif

Explanation / Answer

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1 + = 90

2 + = 90

We must have: + = 90

>>>> 1 + 2 = 90    (1)

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n1 sin1 = n2 sin2  

>>>> sin1 = ng sin2

from (1) >>> sin1 = ng sin(90 - 1) >>>> sin1 = ng cos(1)

>>>>> tan1 = ng >>>> 1 = arctan(ng)

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