A ray of light strikes a glass surface at an angle of incidence of 30 degrees. If the refractive index of glass is 1.5, what is the angle of refraction? (2022)
Practice Questions
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Q1
A ray of light strikes a glass surface at an angle of incidence of 30 degrees. If the refractive index of glass is 1.5, what is the angle of refraction? (2022)
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Using Snell's law, n1 * sin(i) = n2 * sin(r). Here, n1 = 1 (air), i = 30 degrees, n2 = 1.5 (glass). Therefore, sin(r) = (1 * sin(30))/1.5 = 0.333. Thus, r = sin^(-1)(0.333) ≈ 19.5 degrees, which is approximately 20 degrees.
Questions & Step-by-step Solutions
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Q
Q: A ray of light strikes a glass surface at an angle of incidence of 30 degrees. If the refractive index of glass is 1.5, what is the angle of refraction? (2022)
Solution: Using Snell's law, n1 * sin(i) = n2 * sin(r). Here, n1 = 1 (air), i = 30 degrees, n2 = 1.5 (glass). Therefore, sin(r) = (1 * sin(30))/1.5 = 0.333. Thus, r = sin^(-1)(0.333) ≈ 19.5 degrees, which is approximately 20 degrees.
Steps: 13
Step 1: Identify the angle of incidence (i), which is given as 30 degrees.
Step 2: Identify the refractive index of air (n1), which is approximately 1.
Step 3: Identify the refractive index of glass (n2), which is given as 1.5.
Step 4: Write down Snell's law formula: n1 * sin(i) = n2 * sin(r).
Step 5: Substitute the known values into the formula: 1 * sin(30 degrees) = 1.5 * sin(r).
Step 6: Calculate sin(30 degrees), which is 0.5.
Step 7: Substitute this value into the equation: 1 * 0.5 = 1.5 * sin(r).
Step 8: Simplify the equation: 0.5 = 1.5 * sin(r).
Step 9: Divide both sides by 1.5 to isolate sin(r): sin(r) = 0.5 / 1.5.
Step 10: Calculate 0.5 / 1.5, which equals approximately 0.333.
Step 11: Use the inverse sine function to find r: r = sin^(-1)(0.333).
Step 12: Calculate sin^(-1)(0.333) to find the angle of refraction, which is approximately 19.5 degrees.
Step 13: Round the angle of refraction to the nearest whole number, which is approximately 20 degrees.
