Reflection and Refraction Question: Red light is incident in air on a 30 degree

Question

Reflection and Refraction Question:

Red light is incident in air on a 30 degree 60 degree 90 degree prism as shown. The incident beam is directed at an angle of phi 1 = 40.9 degree with respect to the horizontal and enters the prism at a height h = 29 cm above the base. The beam leaves the prism to the air at a distance d = 77.9 along the base as shown. Known: phi 2 the angle the beam in the prism makes with the horizontal axis=46.42 degrees n, the index of refraction of the prism for red light=1.39 phi 3,the angle the transmitted beam makes with the horizontal axis=17.06 degrees What is phi max the maximum value of phi 1 for which the incident beam experiences total internal reflection at the horizontal face of the prism? Suppose now that the violet beam is incident at height h, but makes an angle phi 1y = 60 degree with the horizontal. What is phi 3y the angle the transmitted beam makes with the horizontal axis?

Explanation / Answer

Call the bottom left of the prism A.
Call the entry point of the light ray B.
Call the exit point of the light ray C.
Drop a perpendicular from B to AC to meet AC at P
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1)
In triangle ABP:
tan(30) = h/AP
AP = 19/tan(30) = 32.91cm

In triangle PBC:
PC = AC - AP = 77.9 - 32.91 = 45 cm
tan(si2) = h/PC = 29/45 -= 0.644
si(2) = arctan(1.293) = 32.78
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2)
Angle ABC = 180 - 30 - 52.3 = 117.22
Draw the normal at point B
Mark the angle of refraction at B as beta.
beta = 117.22 - 90 = 17.22

From the diagram you should see:
The angle of incidence, alfa = 90 - 30 - (si)1 = 60 - 40.9 = 11.1

From Snell's law
Refractive index, u = sin(alfa)/sin(beta) = sin(11.1)/sin(17.22) = 0.65
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3) Find the angle of incidence in the glass at point C, then use Snell's law to find the angle of refraction in the air. Then find %u03C6%u2083
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4) Work out the critical angle in the glass. Then use this and geometry to work out the angle of refraction at point B. Then use Snell's law to work out the angle of incidence at point B. Then you can find %u03C6%u2081-max
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5) Can't do this without knowing the refractive index for violet light. If you have this information, you have to work-rthe calculations using the same methods as above.

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