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 slit separation of 0.1 mm and a screen distance of 1 m?
300 nm
600 nm
450 nm
750 nm
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 slit separation of 0.1 mm and a screen distance of 1 m?
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 easier calculations. 0.1 mm = 0.1 / 1000 = 0.0001 m.
Step 3: Recall 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: Rearrange the formula to solve for wavelength (λ): λ = d sin(θ) / m.
Step 5: Calculate sin(30°). The sine of 30 degrees is 0.5.
Step 6: Substitute the values into the formula: λ = (0.0001 m) * (0.5) / 1.
Step 7: Perform the multiplication: λ = 0.0001 m * 0.5 = 0.00005 m.
Step 8: Convert the wavelength back to mm: 0.00005 m = 0.05 mm.
Step 9: Convert the wavelength from mm to nanometers (1 mm = 1,000,000 nm): 0.05 mm = 0.05 * 1,000,000 nm = 500 nm.
