1) 2) 3) 4) 5) 6) Red light is incident in air on a 30 degree - 60 degree - 90 d
ID: 2251025 • Letter: 1
Question
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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 ?1 = 46 degree with respect to the horizontal and enters the prism at a height h = 21 cm above the base. The beam leaves the prism to the air at a distance d = 53.4 along the base as shown. What is ?2, the angle the beam in the prism makes with the horizontal axis? What is n, the index of refraction of the prism for red light? What is ?3, the angle the transmitted beam makes with the horizontal axis? What is ?1,max, the maximum value of ?1 for which the incident beam experiences total internal reflection at the horizontal face of the prism? The red beam is now replaced by a violet beam that is incident at the same angle ?1 and same height h. The prism has an index of refraction nviolet = 1.65 for violet light. Compare dviolet, the exit distance for violet light, to d, the exit distance for red light. Suppose now that the violet beam is incident at height h, but makes an angle ?1,v = 60o with the horizontal. What is ?3,v, the angle the transmitted beam makes with the horizontal axis?Explanation / Answer
(Note: You used 47.6degrees as an angle and 47.6cm as a length. The 2 numbers are the same - this may be a coincidence or you might have transcribed the question wrongly. I've used the values you stated.)
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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In triangle ABP:
tan(30?) = h/AP
AP = 19/tan(30?) = 32.91cm
In triangle PBC:
PC = AC - AP = 47.6 - 32.91 = 14.69cm
tan(??) = h/PC = 19/14.69 -= 1.293
?? = tan?
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