What is the wavelength of light if the first-order maximum occurs at an angle of
Practice Questions
Q1
What is the wavelength of light if the first-order maximum occurs at an angle of 30° in a double-slit experiment with a slit separation of 0.1 mm and a screen distance of 1 m? (2019)
0.5 mm
0.3 mm
0.2 mm
0.1 mm
Questions & Step-by-Step Solutions
What is the wavelength of light if the first-order maximum occurs at an angle of 30° in a double-slit experiment with a slit separation of 0.1 mm and a screen distance of 1 m? (2019)
Step 1: Identify the given values from the problem. We have the slit separation (d) = 0.1 mm, the angle (θ) = 30°, and the order of maximum (m) = 1.
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 wavelength (λ) in a double-slit experiment: λ = d * sin(θ) / m.
Step 4: Calculate sin(30°). The value of sin(30°) is 0.5.
Step 5: Substitute the values into the formula: λ = 0.0001 m * 0.5 / 1.
Step 6: Perform the multiplication: λ = 0.0001 m * 0.5 = 0.00005 m.
Step 7: Convert the wavelength back to mm for the final answer: 0.00005 m = 0.00005 * 1000 = 0.05 mm.
