In the ray diagram of the figure, where the angles are not drawn to scale, the r

Question

In the ray diagram of the figure, where the angles are not drawn to scale, the ray is incident at the critical angle on the interface between materials 2 and 3. Angle ? = 60.6o, and two of the indexes of refraction are n1 = 1.71 and n2 = 1.63. Find (a) index of refraction n3 and (b) angle ?. (c) If ? is decreased, does light refract into material 3?

Chapter 33, Problem 067 In the ray diagram of the figure, where the angles are not drawn to scale, the ray is incident at the critical angle on the interface between materials 2 and 3. Angle = 60.60, and two of the indexes of refraction are n1 = 1.71 and n2 = 1.63. Find (a) index of refraction n3 and (b) angle . (c) If is decreased, does light refract into material 3? ns (a) Number Units (b) Number Units

Explanation / Answer

We have

theta = sin inverse ( n3/n2)

so, n3 = n2*sin theta = 1.63*sin 60.6 = 1.42

b)

n2 sin 29.4 = n1 * sin theta1

theta 1 = sin inverse (n2 sin 29.4 / n1)

theta 1 = 27.9 degrees

c)

If is decreased, will increase, and thus cause the ray to strike the interface (between
materials 2 and 3 ) at an angle larger than critical angle.

Therefore, no transmission of light into material 3 can occur.

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