Worksheet: Critical Angle for Total Internal Reflection

In this worksheet, we will practice relating the paths of refracted and internally reflected light rays to the refractive index of media they travel in.

Q1:

Which of the following formulas correctly shows the relation between the critical angle for total internal reflection πœƒ  for a light ray, the refractive index 𝑛  of the substance the light is propagating in, and the refractive index 𝑛  of the substance when the light is reflected from its surface?

  • A πœƒ = 𝑛 𝑛   
  • B s i n πœƒ = 𝑛 𝑛   
  • C s i n s i n πœƒ = ο€½ 𝑛 𝑛    
  • D s i n πœƒ = 𝑛 𝑛   
  • E πœƒ = ο€½ 𝑛 𝑛     s i n

Q2:

What is the critical angle for a light ray traveling in water with a refractive index of 1.33 that is incident on the surface of water above which air is with a refractive index of 1.00? Answer to the nearest degree.

Q3:

What is the critical angle for a light ray traveling in water with a refractive index of 1.33 that is incident on the surface of water above which ice is with a refractive index of 1.31? Answer to the nearest degree.

  • A 8 0 ∘
  • B 4 5 ∘
  • C 9 . 9 ∘
  • D 9 0 ∘
  • E 3 7 ∘

Q4:

Light rays travel through kerosene. A layer of water that has a refractive index of 1.33 floats on the surface of the kerosene. Light rays that are incident on the interface of kerosene and water at angles of 1 6 . 9 ∘ from the surface or less are totally internally reflected. What is the refractive index of the kerosene? Answer to three significant figures.

  • A1.39
  • B1.27
  • C4.58
  • D2.57
  • E3.64

Q5:

The critical angle required for total internal reflection at a boundary between two substances is 3 0 ∘ . The refractive index of the medium that light is reflected from is 1.1. What is the difference between the refractive index of the medium from which the light is reflected and the refractive index of the medium in which the light propagates before it is reflected?

  • A2.5
  • B2.2
  • C1.1
  • D1.9
  • E4.4

Q6:

Light rays take the paths shown in the diagram between substances with refractive indexes 𝑛  , 𝑛  , and 𝑛  . Three paths are shown for the hypothetical raysβ€”ray I, ray II, and ray IIIβ€”that emerge from the substance with the refractive index 𝑛  into the substance with the refractive index 𝑛  .

Which of 𝑛  , 𝑛  , and 𝑛  is the largest refractive index?

  • A 𝑛 
  • B 𝑛 
  • C 𝑛 

Which of 𝑛  , 𝑛  , and 𝑛  is the smallest refractive index?

  • A 𝑛 
  • B 𝑛 
  • C 𝑛 

Which of ray I, ray II, and ray III correctly shows the path that light would take?

  • ARay II
  • BRay I
  • CRay III

Q7:

The diagram shows a light ray that is transmitted from substance I to substance II at angle πœƒ  to the boundary between the substances. The ray is totally internally reflected back into substance II at the boundary to substance III. For any angle of πœƒ greater than πœƒ  , the light ray is transmitted to substance III. Find the angle πœƒ  to the nearest degree.

  • A 3 4 ∘
  • B 4 1 ∘
  • C 2 8 ∘
  • D 4 9 ∘
  • E 5 7 ∘

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