If the distance between the slits in a double-slit experiment is halved, what happens to the angular position of the first-order maximum? (2023)
Practice Questions
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Q1
If the distance between the slits in a double-slit experiment is halved, what happens to the angular position of the first-order maximum? (2023)
It doubles
It halves
It remains the same
It quadruples
If the slit separation d is halved, the angle θ for the first-order maximum (d sin θ = λ) will increase, effectively doubling the angle.
Questions & Step-by-step Solutions
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Q
Q: If the distance between the slits in a double-slit experiment is halved, what happens to the angular position of the first-order maximum? (2023)
Solution: If the slit separation d is halved, the angle θ for the first-order maximum (d sin θ = λ) will increase, effectively doubling the angle.
Steps: 7
Step 1: Understand the double-slit experiment. It involves light passing through two slits and creating a pattern of bright and dark spots on a screen.
Step 2: Know that the position of these bright spots (maxima) is determined by the formula d sin θ = nλ, where d is the distance between the slits, θ is the angle to the maximum, n is the order of the maximum (1 for first-order), and λ is the wavelength of the light.
Step 3: If the distance between the slits (d) is halved, we can write this as d' = d/2.
Step 4: Substitute d' into the formula: (d/2) sin θ' = nλ, where θ' is the new angle for the first-order maximum.
Step 5: Rearranging gives us sin θ' = (2nλ)/d. Since n is 1 for the first-order maximum, we have sin θ' = (2λ)/d.
Step 6: Compare this with the original equation for the first-order maximum: sin θ = (λ)/d. Notice that sin θ' = 2 * sin θ.
Step 7: Since sin θ' is double sin θ, the angle θ' must increase, effectively doubling the angle for the first-order maximum.
