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A ray of light passes from air into water. If the angle of incidence is 30 degre

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Question: A ray of light passes from air into water. If the angle of incidence is 30 degrees, what is the angle of refraction in water (n = 1.33)?

Options:

  1. 22.5 degrees
  2. 30 degrees
  3. 22 degrees
  4. 40 degrees

Correct Answer: 22.5 degrees

Solution: 

Using Snell\'s law: n1 * sin(θ1) = n2 * sin(θ2). Here, sin(30) = 0.5, so sin(θ2) = (1 * 0.5) / 1.33 = 0.375. Thus, θ2 = sin^(-1)(0.375) ≈ 22.5 degrees.

A ray of light passes from air into water. If the angle of incidence is 30 degre

Practice Questions

Q1
A ray of light passes from air into water. If the angle of incidence is 30 degrees, what is the angle of refraction in water (n = 1.33)?
  1. 22.5 degrees
  2. 30 degrees
  3. 22 degrees
  4. 40 degrees

Questions & Step-by-Step Solutions

A ray of light passes from air into water. If the angle of incidence is 30 degrees, what is the angle of refraction in water (n = 1.33)?
  • Step 1: Identify the given values. The angle of incidence (θ1) is 30 degrees, and the refractive index of air (n1) is approximately 1.0, while the refractive index of water (n2) is 1.33.
  • Step 2: Write down Snell's law formula: n1 * sin(θ1) = n2 * sin(θ2).
  • Step 3: Substitute the known values into the formula: 1.0 * sin(30 degrees) = 1.33 * sin(θ2).
  • Step 4: Calculate sin(30 degrees). It equals 0.5.
  • Step 5: Substitute sin(30 degrees) into the equation: 1.0 * 0.5 = 1.33 * sin(θ2).
  • Step 6: Simplify the equation: 0.5 = 1.33 * sin(θ2).
  • Step 7: Solve for sin(θ2) by dividing both sides by 1.33: sin(θ2) = 0.5 / 1.33.
  • Step 8: Calculate 0.5 / 1.33, which equals approximately 0.375.
  • Step 9: Find θ2 by taking the inverse sine (sin^(-1)) of 0.375: θ2 = sin^(-1)(0.375).
  • Step 10: Calculate sin^(-1)(0.375) to find θ2, which is approximately 22.5 degrees.
  • Refraction – The bending of light as it passes from one medium to another, governed by Snell's law.
  • Snell's Law – A formula used to describe the relationship between the angles of incidence and refraction and the indices of refraction of the two media.
  • Index of Refraction – A dimensionless number that describes how fast light travels in a medium compared to vacuum.
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