1.) As shown in the figure, a light ray enters a slab made of an unknown transpa

Question

1.) As shown in the figure, a light ray enters a slab made of an unknown transparent material at point A at incident angle ? = 32.2° and then undergoes total internal reflection at point B. What minimum value for the index of refraction of the transparent material can be inferred from this information?

2) The figure depicts a simplistic optical fiber: a plastic core (n1 = 1.59) is surrounded by a plastic sheath (n2 = 1.52). A light ray is incident on one end of the fiber at angle ?. The ray is to undergo total internal reflection at point A, where it encounters the core-sheath boundary. (Thus there is no loss of light through that boundary.) What is the maximum value of ? that allows total internal reflection at A?

Explanation / Answer

1) Refractive index o air n2 = 1

From snells law n1sin1 = n2sin2

For total internal reflection 2 =90 degrees

n1*sin(32.2) = 1*sin(90)

n1 = 1.877

2) n1 =1.59 , n2 =1.51

From snells law n1sin1 = n2sin2

For total internal reflection 2 =90 degrees

1.59*sin1 = 1.51*sin(90)

1 = 71.75 degrees

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