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 solve this problem, we can use the formula for the fringe spacing, which is given by:
d = λ * D / L
Where:
- d is the fringe spacing on the screen,
- λ is the wavelength of light,
- D is the distance between the slits and the screen,
- L is the distance between the slits.
In this problem, we are given:
- λ = 589 nm (or 0.589 mm),
- d = 4.0 mm,
- D = 150 cm (or 1500 mm).
We need to find L, the spacing between the two slits. Rearranging the formula, we have:
L = d * L / (λ * D)
Substituting the given values:
L = 4.0 mm * 1500 mm / (0.589 mm * 1500 mm)
Canceling out the units, we get:
L = (4.0 * 1500) / 0.589
Evaluating the expression, we find:
L ≈ 10,208 mm
Therefore, the spacing between the two slits is approximately 10,208 mm, or 1.0 x 10^4 mm (rounded to two significant figures).