SOLUTION: Please help me with this word problem. The index of refraction {{{ n }}} of a transparent material is the ratio of the speed of light in a vacuum to the speed of light in the ma

Question 1067578: Please help me with this word problem.
The index of refraction of a transparent material is the ratio of the speed of light in a vacuum to the speed of light in the material. For the triangular prism in the picture, n = 1.5 and a = 60�. Identify the angle θ for the glass prism if ( see image linked below ) thanks a bunch.
image: https://s28.postimg.org/q8pbxbknx/word_problem.png
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The picture:

= prism angle crossed by the light

= angle of deviation of the light as it goes through the prism

To calculate we need the trigonometric identity formula for a sum of angles:
.

So substituting the expression above,
and the value for
in the formula for refractive index, we get
.
Multiplying both sides of the equal sign times ,
we get the equivalent equation

Now, dividing both sides of the equation by ,
we get the equivalent equation
,
which simplifies to
,
so
--> -->
From
, or the more elegantly written equivalent
,
we can calculate an approximate value for ,
for which your calculator would give you an approximate value for ,
which can be used to calculate an approximate value for .
The approximate values would be:
, ,
and .

An exact value would have to be expressed as an inverse tangent function
,
or if you use the double angle trigonometric identity to calculate that ,
.
Hopefully no instructor would make you go through all that trouble.
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