ForMicro

Question 1

If you consider the speed of light in vacuum c = 3 × 10^8 m/s, what is the speed of light in a material of refractive index n=1.5

Answer 1

C. 2 × 10^8 m/s

By definition, we have n = c
v, with v being the speed of light in the material.
So v = c
n = 3×10^8
1.5 = 2 × 10^8 m/s

Question 2

A ray of light travels in a material of index n 1 =1.40. It reaches the interface with a second medium of index n 2 =1.50 at an angle i1 =45o with the normal. What is the refracted angle the light forms with the normal after crossing the interface?

Answer 2

D. 41o
The second medium has a refractive index higher than the first one, so there will always be refraction. Snell’s law dictates n1 sin i1 = n2 sin i2, so we have i2 = arcsin ((n1/n2)sin i1) = arcsin ((1.4/1.5) sin(45°)) = 41°

Question 3

A ray of light travels in a material of index n 1 =1.60. It reaches the interface with a second medium of index n 2 =1.50 at an angle i1 =65.0o with the normal. What happens to the light?

Answer 3

B. It is refracted at an angle of 75.2o

The second medium has a lower index than the first medium, so there is a critical angle ic for refraction.

ic = asin n2/n1
= asin (1.5/1.6) = 69.6°

The incoming angle i1 is lower than iC, so there is refraction according to Snell’s law.

i2 = asin ((n1/n2) sin i1) = asin ((1.6/1.5) sin(65°)) = 75.2°

Question 4

A ray of light travels in a material of index n1 =1.60. It reaches the interface with a second medium of index n2 =1.50 at an angle i1 =75.2o with the normal. What happens to the light?

Answer 4

A. It is reflected at an angle of 75.2o

The second medium has a lower index than the first medium, so there is a critical angle ic for refraction.
ic = asin (n2/n1) = asin (1.5/1.6) = 69.6°

The incoming angle i1 is larger than iC, so there is total reflection. The law of reflection dictates light reflects at the same angle than the incoming angle

Question 5

Which picture represents the correct behavior of light?

The dashed line represents the normal to the interface. The two different shades represent two different propagation media.

Answer 5

The second medium has a refractive index higher than the first one, so there will always be refraction. Because the second medium has a refractive index larger than the one of the first medium, the refraction angle will be smaller than the incoming angle.