Critical Angle Problems
Critical Angle Formula:
Material
Vacuum
Air
Water
Ethyl Alcohol
Acryllic
Amber
Mercury
Sapphire
Cubic Zirconium
Diamond
Silicon
𝑛1 𝑠𝑖𝑛(𝜃𝐶 ) = 𝑛2 𝑠𝑖𝑛(90)
Index of Refraction
1
1.00
1.33
1.36
1.50
1.55
1.62
1.77
2.16
2.42
3.96
1) In her bedroom Mia has a fiber optic lamp, which has an index of refraction of
1.48.
a. What is the critical angle, which will allow for total internal reflection
in her lamp?
b. If light enters at an angle of incidence of 50° will her lamp work?
c. If light enters at an angle of incidence of 40° will her lamp work?
2) You are trying to figure out why Verizon’s service is so poor today. Their
signal just won’t come through and that’s not cool because the Millionaire
Matchmaker is on Bravo. Verizon uses a fiber optic cable to send the
television signal to your house. The fiber optic cable has an index of
refraction of 1.6.
a. What is the critical angle, which will allow for total internal reflection
in her lamp?
b. If the signal is not reaching your house what angle of incidence did
they probably send the signal at? 30°, 35° or 50°?
c. Is the signal refracting or totally internally reflecting?
3) The critical angle for a certain liquid-air surface is 47.7 degrees.
a. What is the index of refraction of this liquid?
b. And what liquid is it?
c. If light is shined through the liquid an angle of 50 degrees to the
normal line will it totally internally reflect or pass into the other
medium?
4) The critical angle for a certain liquid-solid surface is 27.6 degrees.
a. What is the index of refraction of this liquid?
b. And what solid is it?
c. If light is shined through the liquid an angle of 40 degrees to the
boundary will it totally internally reflect or pass into the other
medium?
Answers:
1)
2)
3)
4)
42.53°
38.68°
ethyl alcohol
cubic zirconium