Answer:
d = 0.597 10⁻⁶ m
Explanation:
In the double slit experiment, the expression for contractive interference is
d sin θ = n λ
Where d is the separation of the slits, n is in integer and the wavelength is
If the observation point (photodetector) is at 1.00 m we can use trigonometry
tan θ = y / L
But in general this experiment measures very small angles so that T = no T, so we substitute in the first equation
d (y / L) = n λ
We can clear ‘and’ from the equation and solve for each wavelength
y = n L λ / d
In this case it tells us that we are in first order (n = 1)
Line 1
y1 = 1.00 588.9950 10⁻⁹ / d
Line 2
y2 = 1.00 589.5924 10⁻⁹ / d
The separation between the two lines 1,000 mm = 1,000 10-3 m
y2-y1 = (589.5924 10⁻⁹ - 588.9950 10⁻⁹) / d
d = 0.5974 10⁻⁹ / (y2-y1)
d = 0.5974 10-9 / 1,000 10-3
d = 0.597 10⁻⁶ m
It is more common to give it in millimeters
d = 0.597 10⁻³ mm = 0.597 μm
