Problem 17.8
Light from a sodium lamp (wavelenght = 589) illuminates two narrow slits. The fringe spacing on a screen 150 cm behind the slits is 4.0 mm .
Part A -
What is the spacing (in mm ) between the two slits?
Express your answer using two significant figures.
To find the spacing between the two slits, we can use the equation for fringe spacing:
Spacing = (wavelength * distance) / fringe spacing
Given:
Wavelength (λ) = 589 nm = 589 * 10^-9 m
Distance (d) = 150 cm = 150 * 10^-2 m
Fringe spacing (s) = 4.0 mm = 4.0 * 10^-3 m
Substituting these values into the equation:
Spacing = (589 * 10^-9 * 150 * 10^-2) / (4.0 * 10^-3)
Spacing = (0.08835) / (0.004)
Spacing ≈ 22.09 mm
Therefore, the spacing between the two slits is approximately 22.09 mm.
To find the spacing between the two slits, we can use the formula for the fringe spacing:
d*sinθ = m*λ
Where:
- d is the spacing between the slits
- θ is the angle of the fringe
- m is the order of the fringe
- λ is the wavelength of the light
In this case, the wavelength of the light is given as 589 nm (or 589*10^-9 m). The fringe spacing on the screen is given as 4.0 mm (or 4.0*10^-3 m). We need to find the spacing between the slits (d).
First, let's convert the given values to SI units:
λ = 589*10^-9 m
Fringe spacing = 4.0*10^-3 m
Now, let's rearrange the formula to solve for d:
d = (m*λ) / sinθ
Since the problem only gives us the fringe spacing and doesn't provide any information about the angle or order, we'll assume that we're observing the central fringe (m = 0) and the angle is small. In this case, sinθ ≈ θ, and we can rewrite the formula as:
d = m*λ / θ
Using the given values and assuming m = 0, we have:
d = (0 * 589*10^-9 m) / θ
Since θ is small, we can use the approximation θ ≈ tanθ ≈ sinθ. Therefore, we can rewrite the formula as:
d = 0 * 589*10^-9 m / θ ≈ 0
This means that we can't determine the spacing between the two slits using the given information because the formula requires the angle or order of the fringe.