Question

Red light is incident in air on a 30o - 60o - 90 o prism as shown. The incident beam is directed at an angle of φ1 = 41.6o with respect to the horizontal and enters the prism at a height h = 23 cm above the base. The beam leaves the prism to the air at a distance d = 61.3 along the base as shown.

1)
What is φ2, the angle the beam in the prism makes with the horizontal axis?

2)
What is n, the index of refraction of the prism for red light?

3)
What is φ3, the angle the transmitted beam makes with the horizontal axis?

4)
What is φ1,max, the maximum value of φ1 for which the incident beam experiences total internal reflection at the horizontal face of the prism?

5)
The red beam is now replaced by a violet beam that is incident at the same angle φ1 and same height h. The prism has an index of refraction nviolet = 1.5 for violet light. Compare dviolet, the exit distance for violet light, to d, the exit distance for red light.

6)
Suppose now that the violet beam is incident at height h, but makes an angle φ1,v = 60o with the horizontal. What is φ3,v, the angle the transmitted beam makes with the horizontal axis?

Answer 1

nal Normal 60 6o 41.60 € $+3 30' 90-6 23cm 30 ra d d 61.3cm 23 X = tan 30 61.3 – x= 23 tan 02 02 -1 = tan = = 46.98° (61.3 23 23 tan 30 from Snell's law ng sin(60 – $, ) = nsino (1) X sin (60 – 41.6) = nsin (60 – 2) n = 1.4 3. Snell's law nsin (90 – 02) = ng sin(90 – 03) 03 – 90 – sin-! {(1.4) * sin(90 – 46.98)} – 17.2° 4. for total internal reflection

90 – 02 Zic ic is the critical argue ic sin = 45.585° 90 – 02 = 45.585° 02 = 90 – 45.585 02 = 44.415 (1) X sin (60 – 41.6) = nsin (60 - 02) (1) x sin (60 – º,) = 1.4 x sin(60 – 44.415) Di -1 ~ 60 – sin {1.4 x sin(60 – 44.415)} = 37.9° 0, ºlmax = 37.9° 5. п, = 1.5 (1) * sin(60 – 41.6) = (1.5) * sin(60 – 02) 02 – 60 – sin-" (sin(60 = 41.6); – 47.852 1.5 23 X = tan 30 23 du - X= tan 47.852 23 23 + tan 47.852 dy = 60.654cm 6.

GO 30 30 ao-Ozv from Snell's law (1.5) < sin 30 = (1) X sin (90 – 03v) 03v = 90 – sin --{(1.5) (sin 30)} - 41.4° 030

Answer 2

Here is a video link to the solution http://youtu.be/YHWkjTjDXrA