One of Mr. Chowder's lab groups is staying after school to complete the Young's Experiment investigation. They observe that light through passing two slits travels 3.93 m to a screen to produce a pattern of bright and dark bands. The group measures the distance between the first and the second bright bands on the same side of the pattern to be 18.8 mm. The slits are spaced 0.132 mm apart. What is the wavelength (in nanometers) of the light source?Wavelengthnm
Question
One of Mr. Chowder's lab groups is staying after school to complete the Young's Experiment investigation. They observe that light through passing two slits travels 3.93 m to a screen to produce a pattern of bright and dark bands. The group measures the distance between the first and the second bright bands on the same side of the pattern to be 18.8 mm. The slits are spaced 0.132 mm apart. What is the wavelength (in nanometers) of the light source?Wavelengthnm
Solution
To solve this problem, we can use the formula for Young's double-slit experiment, which is:
λ = (yd) / (mL)
where:
- λ is the wavelength of the light,
- y is the distance between the bright bands,
- d is the distance between the slits,
- m is the order of the bright band (in this case, m=1 because we are looking at the distance between the first and second bright bands),
- L is the distance from the slits to the screen.
First, we need to convert the measurements to the same units. The distance between the bright bands (y) is given in mm, so we convert it to meters: 18.8 mm = 0.0188 m.
The distance between the slits (d) is also given in mm, so we convert it to meters: 0.132 mm = 0.000132 m.
The distance from the slits to the screen (L) is already given in meters: 3.93 m.
Now we can substitute these values into the formula:
λ = (0.0188 m * 0.000132 m) / (1 * 3.93 m)
Solving this gives λ = 6.32 x 10^-7 m.
To convert this to nanometers, we multiply by 10^9 (since 1 m = 10^9 nm), giving a final answer of λ = 632 nm.
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