- #1
julianwitkowski
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Homework Statement
A laser emitting light with a wavelength of 560 nm is directed at a single slit, producing an interference pattern on a screen that is 3.0 m away. The central maximum is 5.0 cm wide. Determine the width of the slit.
I have two ideas of the answer but I'm not sure which is right... Please help me understand which one and why.
Homework Equations
[/B]
d = λ / sin(Θ)
tan(Θ) = x / L
or...
w = λL / y
The Attempt at a Solution
[/B]
Attempt #1
d = slit width
λ = wavelength (560nm = 5.6· 10⁻⁷m)
Θ = angle
If the central maximum is 5.0cm wide, then is the distance from the center to the first minimum always half of that or 2.5cm?
tan(Θ) = 0.025m / 3m
Θ = tan⁻¹ (0.025m / 3m) = 0.477°
d · sin(Θ) = λ
d = λ / sin(Θ) = 560nm /sin(0.477°) = 5.6· 10⁻⁷m / sin(0.477°) = 6.72 · 10⁻⁵ m = 67200 nm
Attempt #2
d = slit width
λ = wavelength (560nm = 5.6· 10⁻⁷m)
L = distance to screen.
y = central maximum.
w = λL / y = 5.6 ·10⁻⁷m · 3m / 0.05m = 3.36 · 10⁻⁵ m = 33600nm