In Figure (a), a beam of light in material 1 is incident on a boundary at an ang

Question

In Figure (a), a beam of light in material 1 is incident on a boundary at an angle 0! = 39degree. Some of the light travels through material 2, and then some of it emerges into material 3. The two boundaries between the three materials are parallel. The final direction of the beam depends, in part, on the index of refraction n3 of the third material. Figure (b) gives the angle of refraction 03 in that material versus n3 for a range of possible n3 values. The vertical axis scale is set by 6-$a = 27degree and 63^ = 51degree. (a) What is the index of refraction of material 1, or is the index impossible to calculate without more information (enter "0")? (b) What is the index of refraction of material 2, or is the index impossible to calculate without more information (enter "0")? (c) If is changed to 70 degree and the index of refraction of material 3 is 2.8, what is 03?

Explanation / Answer

a.)

By snell's law -

sin(x2)/sin(x1) = n1/n2   .........[equ1]

sin(x3)/sin(x2) = n2/n3   .........[equ2]

equ1*equ2

sin(x3)/sin(x1) = n1/n3

for n3=1.6, x3 = (51+27)/2 degrees = 39 degrees

Hence,

sin(39)/sin(39) = n1 / 1.6

n1 = 1.6

b.)

We have 2 dependent equations. We can't find n2

0

c.)

sin(x3)/sin(70) = 1.6/2.8

sin(x3) = (1.6/2.8)sin(70)

x3 = 32.4774 degrees

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