A student performs Young's double-slit experiment using a slit separation of 20.1 μm. A screen is placed 3.00 m from the centre of the sources such that a point on the fifth nodal line is 35.5 cm from the centre of the interference pattern. Find the wavelength of the light used and identify its colour. Thank you!
To find the wavelength of the light used in Young's double-slit experiment, we can use the formula:
λ = (m * d) / L
Where:
λ is the wavelength of the light,
m is the order of the nodal line (in this case, m = 5),
d is the slit separation,
L is the distance from the slits to the screen.
Given:
d = 20.1 μm = 20.1 x 10^(-6) m (convert from micrometers to meters)
L = 3.00 m
m = 5
We can substitute these values into the formula to find the wavelength:
λ = (5 * 20.1 x 10^(-6) m) / (3.00 m)
Simplifying,
λ = 0.0335 x 10^(-6) m
To identify the color of light based on its wavelength, we can refer to the visible light spectrum. The visible light spectrum ranges from approximately 400 nm (violet) to 700 nm (red).
Converting our wavelength to nanometers (nm):
λ = 0.0335 x 10^(-6) m * 10^9 nm/1 m
λ ≈ 33.5 nm
Based on the wavelength of approximately 33.5 nm, it does not correspond to any specific visible color. It is in the ultraviolet (UV) range, which is not visible to human eyes.