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A ray of light passes from air into water at an angle of incidence of 30 degrees

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Question: A ray of light passes from air into water at an angle of incidence of 30 degrees. What is the angle of refraction in water? (Refractive index of water = 1.33)

Options:

  1. 22.5 degrees
  2. 30 degrees
  3. 40 degrees
  4. 20 degrees

Correct Answer: 22.5 degrees

Solution: 

Using Snell\'s law, n1 * sin(θ1) = n2 * sin(θ2), we find θ2 = sin^(-1)(sin(30 degrees)/1.33) = 22.5 degrees.

A ray of light passes from air into water at an angle of incidence of 30 degrees

Practice Questions

Q1
A ray of light passes from air into water at an angle of incidence of 30 degrees. What is the angle of refraction in water? (Refractive index of water = 1.33)
  1. 22.5 degrees
  2. 30 degrees
  3. 40 degrees
  4. 20 degrees

Questions & Step-by-Step Solutions

A ray of light passes from air into water at an angle of incidence of 30 degrees. What is the angle of refraction in water? (Refractive index of water = 1.33)
  • Step 1: Identify the given information. We have an angle of incidence (θ1) of 30 degrees and the refractive index of water (n2) as 1.33. The refractive index of air (n1) is approximately 1.
  • Step 2: Write down Snell's law formula: n1 * sin(θ1) = n2 * sin(θ2).
  • Step 3: Substitute the known values into the formula: 1 * sin(30 degrees) = 1.33 * sin(θ2).
  • Step 4: Calculate sin(30 degrees). We know that sin(30 degrees) = 0.5.
  • Step 5: Substitute this value into the equation: 1 * 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 the value: sin(θ2) ≈ 0.3759.
  • Step 9: Find θ2 by taking the inverse sine: θ2 = sin^(-1)(0.3759).
  • Step 10: Calculate θ2 to find the angle of refraction in water, which is approximately 22.5 degrees.
  • Refraction – The bending of light as it passes from one medium to another due to a change in speed.
  • Snell's Law – A formula used to describe the relationship between the angles of incidence and refraction when light passes between two different media.
  • Refractive Index – A dimensionless number that describes how fast light travels in a medium compared to vacuum.
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