Worksheet: Deviation due to a Prism

In this worksheet, we will practice determining the effect of the shape and refractive index of a prism on the path taken through it by light rays.

Q1:

A triangular prism has an apex angle of 48. The prism produces a minimum angle of deviation of light rays through it when the angle of incidence of light rays onto the prism is 36. What is the minimum angle of deviation of the prism? Answer to the nearest degree.

Q2:

A triangular prism produces a minimum angle of deviation of light rays through it when the angle of incidence of light rays onto the prism is 44. The minimum angle of deviation of the prism is 28. What is the apex angle of the prism? Answer to the nearest degree.

Q3:

A very thin triangular prism has an apex angle of 2.5. The minimum deviation angle through the prism is 1.4. Find the refractive index of the prism using the small-angle approximation. Answer to one decimal place.

Q4:

A triangular prism has an apex angle of 77. Given that the angle of minimum deviation is 44 and light rays deviate least through the prism at an angle of incidence of 44, find the refractive index of the prism to 2 decimal places.

Q5:

A very thin triangular prism has an apex angle of 2.8. The refractive index of the prism is 1.4. Find the minimum angle of deviation produced by the prism using the small-angle approximation. Answer to one decimal place.

Q6:

The diagram shows the path of a light ray through a triangular prism. The apex angle of the prism 𝜃=40. What is the angle Φ? Answer to the nearest degree.

Q7:

The graph shows how the angle of deviation of the triangular prism shown in the diagram varies with the angle of incidence of light rays on it.

Where 𝛼, the angle of deviation, has its minimum value, which of the angles in the diagram is equal to the angle Φ?

  • A𝐴
  • B𝛼
  • CΦ
  • D𝜃
  • E𝜃

Where 𝛼, the angle of deviation, has its minimum value, which of the angles in the diagram is equal to the angle 𝜃?

  • A𝜃
  • B𝐴
  • CΦ
  • D𝛼
  • EΦ

Q8:

The diagram shows the path of a light ray through a triangular prism. What is the sum of the angles 𝑎 and 𝑏?

Q9:

The diagram shows the path of a light ray through a triangular prism. Which of the following correctly relates the apex angle of the prism 𝐴 to the angles of incidence and the angles of refraction of the incident and emergent rays shown?

  • A180(𝜃+Φ)=𝐴
  • BΦ+𝜃=𝐴
  • CΦ+Φ=𝐴
  • D𝜃+𝜃=𝐴
  • E𝜃+Φ=𝐴

Q10:

A triangular prism has an apex angle of 45. The minimum angle of deviation of the prism is 55. What is the angle of incidence that corresponds to this angle of deviation? Answer to the nearest degree.

Q11:

Which of the following formulas correctly relates 𝛼, the minimum deviation angle of a triangular prism, to 𝜙, the angle of incidence of light onto the prism that corresponds to the minimum deviation angle, and 𝐴, the apex angle of the prism?

  • A𝜙=𝛼+𝐴2
  • B𝜙=𝛼+𝐴
  • C𝜙=𝛼2+𝐴
  • D𝜙=2(𝛼+𝐴)
  • E𝜙=(𝛼+𝐴)2

Q12:

The diagram shows the path of a light ray through a triangular prism. Which of the following is a correct formula for determining the angle 𝛼?

  • A𝛼=Φ+𝜃+𝐴
  • B𝛼=Φ+𝜃𝐴
  • C𝛼=Φ+𝜃𝐴
  • D𝛼=Φ𝜃+𝐴
  • E𝛼=Φ+𝜃+𝐴

Q13:

Which of the following formulas correctly relates 𝛼, the minimum deviation angle of light rays through a triangular prism that is in air, to 𝐴, the apex angle of the prism, and 𝑛, the refractive index of the prism?

  • A𝑛=((2𝐴))sinsin()
  • B𝑛=sinsin()
  • C𝑛=((2(𝛼+𝐴)))((2𝐴))sinsin
  • D𝑛=((2(𝛼+𝐴)))sinsin
  • E𝑛=((𝛼+2𝐴))sinsin

Q14:

The graph contains four lines that may or may not correctly represent a plot of how 𝛼, the angle of deviation of the triangular prism shown in the diagram, varies with Φ, the angle of incidence of light rays on it. Which of the lines represents the relationship between Φ and 𝛼 correctly?

  • ARed
  • BBlue
  • CGreen
  • DBlack
  • EYellow

Q15:

The diagram shows the path of three light rays through a prism. The light rays are all the same color.

Which of the following shows the correct order of the sizes of the incident angles 𝐼, 𝐼, and 𝐼?

  • A𝐼<𝐼, 𝐼>𝐼
  • B𝐼<𝐼<𝐼
  • C𝐼>𝐼>𝐼
  • D𝐼>𝐼, 𝐼>𝐼
  • E𝐼<𝐼, 𝐼>𝐼

Which of the following shows the correct order of the sizes of the deviation angles 𝛼, 𝛼, and 𝛼?

  • A𝛼>𝛼>𝛼
  • B𝛼>𝛼>𝛼
  • C𝛼>𝛼>𝛼
  • D𝛼>𝛼>𝛼
  • E𝛼>𝛼>𝛼

Q16:

The diagram shows the path of a light ray passing through a triangular prism with a refractive index of 1.5 that is surrounded by air. The angle Φ=42 and the apex angle of the prism 𝐴=58. Find the angle 𝛼 to the nearest degree.

Q17:

The diagram shows the path of a light ray through a triangular prism. Which of the following is the physical significance of the angle 𝛼?

  • AThe angle 𝛼 is the critical angle of the prism for total internal reflection.
  • BThe angle 𝛼 is the angle through which the direction of the path of a light ray changes due to the ray passing through a prism.
  • CThe angle 𝛼 is directly proportional to the ratio of the base of the prism to the height of the prism.
  • DThe angle 𝛼 is the angle that a prism would have to rotate around its apex in order to produce total internal reflection of the incident ray shown.
  • EThe angle 𝛼 is directly proportional to the refractive index of a prism.

Q18:

The triangular prism shown in the diagram has an apex angle 𝐴 of only a few degrees. The magnified view of the region of the prism through which a light ray passes shows that the angle of deviation 𝛼 is also very small. For such a small angle 𝜃, the approximation can be made so that sin𝜃𝜃. For a very thin prism, the small-angle approximation can be used.

If the small-angle approximation is used with the formula 𝑛=sinsin(), which of the following is a correct approximation to the formula?

  • A𝑛=(𝛼+𝐴)2𝐴
  • B𝑛=2𝐴𝛼
  • C𝑛=𝛼+𝐴2
  • D𝑛=(𝛼+𝐴)𝐴
  • E𝑛=(𝛼+𝐴)2

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