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 (n = 1.33)?

Options:

Correct Answer: 22.5 degrees

Solution:

Using Snell\'s law, n1 * sin(θ1) = n2 * sin(θ2). Here, sin(30) = 0.5, so 1 * 0.5 = 1.33 * sin(θ2). Solving gives θ2 ≈ 22.5 degrees.

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 (n = 1.33)?

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 (n = 1.33)?

Step 1: Identify the given information. We have the angle of incidence (θ1) which is 30 degrees, the refractive index of air (n1) which is approximately 1, and the refractive index of water (n2) which 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 * sin(30 degrees) = 1.33 * sin(θ2).
Step 4: Calculate sin(30 degrees). We know that sin(30 degrees) = 0.5.
Step 5: Substitute sin(30 degrees) into the equation: 1 * 0.5 = 1.33 * sin(θ2).
Step 6: This simplifies to: 0.5 = 1.33 * sin(θ2).
Step 7: To find sin(θ2), divide both sides by 1.33: sin(θ2) = 0.5 / 1.33.
Step 8: Calculate the value: sin(θ2) ≈ 0.3759.
Step 9: Use the inverse sine function to find θ2: θ2 = sin^(-1)(0.3759).
Step 10: Calculate θ2, which gives 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.
Index of Refraction – A dimensionless number that describes how fast light travels in a medium compared to vacuum.