As shown in the figure, white light enters a 45-90-45 crown glass prism at the v

Question

As shown in the figure, white light enters a 45-90-45 crown glass prism at the vertical face. Part of this light refracts at the slanted face into the surrounding material and the rest experiences total internal reflection and exits the prism at the horizontal base. The colors of light that emerge from the slanted face may be chosen by varying the index of refraction of the material surrounding the prism. Determine the required index of refraction of the surrounding material for each of the following cases.

(a) Only red, orange, yellow, and green light refract from the slanted face of the prism into the surrounding material. (Express your answer to 4 significant figures.)

(b) All colors except violet light refract from the slanted face of the prism into the surrounding material. (Express your answer to 4 significant figures.

Color Vacuum Wavelength (nm) Index of Refraction in Crown Glass (nm) Red 660 1.512 Orange 610 1.514 Yellow 580 1.518 Green 550 1.519 Blue 470 1.524 Violet 410 1.530

Explanation / Answer

For the critical angle we ca obtain an equation form snells law,

na sin A = nb Sin B

for ange of incidnce theta > critca ange , rays get total internal reflection.

(a) In the figure, theta1 = 45

inorder to light rays except violet get refracted

theta c for r blue =45(incident angle in the figure).

Because all the other rays except violet has larger theta c because their n1 is smaller.

If theta c for blue=45 then only violet will get total inernally refracted.

So, from snells law n2=sin(45)*1.524

n2 = =1.078

(b) As before, If theta c for orange = 45, then only red and orange will refracted from

slanted face.

So, from (1)

n2=sin(45)*1.51

n2 =1.071

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