Problem 17.8
Light from a sodium lamp (wavelenght = 598) illuminates two narrow slits. The fringe spacing on a screen 150cm 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:
Fringe spacing (d) = (wavelength * distance to screen) / distance between slits
Given:
Wavelength (λ) = 598 nm = 0.598 μm (since 1 nm = 10^-3 μm)
Distance to screen (D) = 150 cm = 1.5 m
Fringe spacing (d) = 4.0 mm = 0.004 m
Rearranging the equation, we have:
Distance between slits = (wavelength * distance to screen) / fringe spacing
Plugging in the values, we get:
Distance between slits = (0.598 μm * 1.5 m) / 0.004 m
Calculating this expression gives:
Distance between slits ≈ 223.5 μm
Converting to mm with two significant figures, the spacing between the two slits is approximately:
Distance between slits ≈ 220 mm
To find the spacing between the two slits, we can use the concept of fringe spacing. The fringe spacing is the distance between consecutive bright or dark fringes on the screen.
In this problem, we are given the fringe spacing (4.0 mm) and the wavelength of light from the sodium lamp (598 nm = 0.598 µm). We can use the simple equation for fringe spacing:
fringe spacing = (wavelength × distance from the slits to the screen) / distance between the slits
We are given the fringe spacing (4.0 mm) and the distance from the slits to the screen (150 cm = 1500 mm). We need to solve for the distance between the slits.
Let's substitute the given values into the equation:
4.0 mm = (0.598 µm × 1500 mm) / distance between the slits
Now, we can solve for the distance between the slits:
distance between the slits = (0.598 µm × 1500 mm) / 4.0 mm
First, let's convert the wavelength from µm to mm:
0.598 µm = 0.598 × 10^-3 mm
Now, substitute this value into the equation:
distance between the slits = (0.598 × 10^-3 mm × 1500 mm) / 4.0 mm
Simplifying the equation further:
distance between the slits = 0.598 × 10^-3 × 1500 / 4.0
distance between the slits ≈ 0.598 × 1500 × 10^-3 / 4.0
distance between the slits ≈ 0.225 mm
Therefore, the spacing between the two slits is approximately 0.225 mm.