Case 3: Diamond-Air. Change the top medium to diamond and keep the bottom medium

Question

Case 3: Diamond-Air. Change the top medium to diamond and keep the bottom medium as air. Fill in the table below.

Diamond ?Air Index of Refraction (Diamond) 2.42
Index of Refraction (Air) 1.0003

Angle of Incidence (degrees) Angle of Reflection (degrees) Angle of Refraction (degrees)
10 10.0 24.8
30 30.0 ----
45 45.0 ----
60 60.0 ----
80 80.0 ----

State the direction in which the refracted ray bends (toward the normal or away from the normal). You can determine this from the diagram or from the comparison of refracted angle to reflected angle.


angle direction
10
30
45
6
80

Explanation / Answer

The Snell's Law of refraction is :

ndiamond sin(diamond) = nair sin(air)   

( represents angle of incidence/refraction, as applicable)

air= sin-1[(ndiamond sin(diamond))/nair]

Since the light is travelling from a denser medium to a rarer medium, therefore, there is a critical angle. Its value is given by :

critical= sin-1(nair/ndiamond) = sin-1(1.0003/2.42) = 24.41 degrees

Therefore, any angle greater than the critical angle will be reflected back into the diamond and will not refract.

(a) For diamond = 30 degrees, the angle of incidence is greater than the critical angle. Therefore, total internal reflection takes place and there is NO angle of refraction. The ray bends away from the outward normal, and into the diamond

(b) For diamond = 45 degrees, the angle of incidence is greater than the critical angle. Therefore, total internal reflection takes place and there is NO angle of refraction. The ray bends away from the outward normal, and into the diamond

(c) For diamond = 60 degrees, the angle of incidence is greater than the critical angle. Therefore, total internal reflection takes place and there is NO angle of refraction. The ray bends away from the outward normal, and into the diamond

(d) For diamond = 80 degrees, the angle of incidence is greater than the critical angle. Therefore, total internal reflection takes place and there is NO angle of refraction. The ray bends away from the outward normal, and into the diamond

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