What is the wavelength of light if the first-order maximum occurs at an angle of 30° in a double-slit experiment with slit separation of 0.1 mm and screen distance of 1 m?
Practice Questions
1 question
Q1
What is the wavelength of light if the first-order maximum occurs at an angle of 30° in a double-slit experiment with slit separation of 0.1 mm and screen distance of 1 m?
0.5 mm
0.6 mm
0.7 mm
0.8 mm
Using d sin θ = mλ, λ = d sin θ/m. For m=1, d=0.1 mm, θ=30°, λ = 0.1 mm * sin(30°) = 0.1 mm * 0.5 = 0.05 mm = 0.5 mm.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the wavelength of light if the first-order maximum occurs at an angle of 30° in a double-slit experiment with slit separation of 0.1 mm and screen distance of 1 m?
Solution: Using d sin θ = mλ, λ = d sin θ/m. For m=1, d=0.1 mm, θ=30°, λ = 0.1 mm * sin(30°) = 0.1 mm * 0.5 = 0.05 mm = 0.5 mm.
Steps: 7
Step 1: Identify the given values from the problem. We have the slit separation (d) = 0.1 mm, the angle (θ) = 30°, and we are looking for the wavelength (λ).
Step 2: Convert the slit separation from mm to meters for consistency. 0.1 mm = 0.1 / 1000 = 0.0001 m.
Step 3: Use the formula for the double-slit experiment: d sin(θ) = mλ, where m is the order of the maximum. For the first-order maximum, m = 1.
Step 4: Calculate sin(30°). The value of sin(30°) is 0.5.
Step 5: Substitute the values into the formula: λ = d sin(θ) / m. This gives us λ = (0.0001 m) * (0.5) / 1.
Step 6: Calculate λ: λ = 0.0001 m * 0.5 = 0.00005 m.
Step 7: Convert λ back to mm for the final answer: 0.00005 m = 0.00005 * 1000 = 0.05 mm.
