Problem 17.8
Light from a sodium lamp (wavelength = 598) 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:
d = λL / D
Where:
d is the fringe spacing (given as 4.0 mm)
λ is the wavelength of light (given as 598 nm, which is equivalent to 0.598 μm)
L is the distance from the slits to the screen (given as 150 cm, which is equivalent to 1500 mm)
D is the distance between the slits (which is what we need to find)
Rearranging the equation, we can solve for D:
D = λL / d
Substituting the given values:
D = (0.598 μm) * (1500 mm) / (4.0 mm)
D = 224.5 μm
To express the answer using two significant figures, we round it to:
D ≈ 220 μm
Therefore, the spacing between the two slits is approximately 220 mm.
To find the spacing between the two slits, we can use the formula for fringe spacing:
λL
d = _____________
x
Where:
d = fringe spacing
λ = wavelength of light
L = distance from the slits to the screen
x = distance between the two slits
Given:
λ = 598 nm = 598 x 10^(-9) m
L = 150 cm = 150 x 10^(-2) m
d = 4.0 mm = 4.0 x 10^(-3) m
Now, let's substitute the values into the formula and solve for x:
(598 x 10^(-9) m)(150 x 10^(-2) m)
x = _____________________________________
4.0 x 10^(-3) m
x = (598 x 150 x 10^(-11) m^2) / (4.0 x 10^(-3) m)
x ≈ 22.425 x 10^(-11) m^2 / 4.0 x 10^(-3) m
x ≈ 5.60625 x 10^(-11) m
Since we want the answer in mm, we need to convert this to mm:
x ≈ (5.60625 x 10^(-11) m) / (10^(-3) m/mm)
x ≈ 5.60625 x 10^(-8) mm
Therefore, the spacing between the two slits is approximately 5.6 x 10^(-8) mm.