Monochromatic light falls on two very narrow slits 0.050 mm apart. Successive fringes on a screen 4.60 m away are 5.7 cm apart near the center of the pattern. Determine the wavelength and frequency of the light.
wavelength nm
frequency Hz
If 540 nm light falls on a slit 0.0490 mm wide, what is the full angular width of the central diffraction peak?
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http://hyperphysics.phy-astr.gsu.edu/Hbase/phyopt/slits.html
To determine the wavelength and frequency of the light, we can make use of the equation for the fringe separation in a double-slit interference pattern:
δy = (λL) / d
where:
δy represents the fringe separation on the screen,
λ represents the wavelength of the light,
L represents the distance between the slits and the screen,
and d represents the separation between the two slits.
Given the following values:
d = 0.050 mm = 0.050 × 10^-3 m (converting millimeters to meters)
δy = 5.7 cm = 5.7 × 10^-2 m (converting centimeters to meters)
L = 4.60 m
Now we can rearrange the equation to solve for the wavelength (λ):
λ = (δy × d) / L
Substituting the values we have:
λ = (5.7 × 10^-2 m × 0.050 × 10^-3 m) / 4.60 m
Calculating this expression gives us the value for the wavelength of the light in meters.
To convert this value to nanometers (nm), we multiply it by 10^9:
λ (in nm) = λ (in meters) × 10^9
Finally, to find the frequency of the light, we can use the equation:
c = λν
where:
c represents the speed of light (approximately 3 × 10^8 m/s),
λ represents the wavelength of the light,
and ν represents the frequency of the light.
We rearrange this equation to solve for the frequency (ν):
ν = c / λ
Substituting the values we have:
ν = (3 × 10^8 m/s) / λ (in meters)
Solve this expression to find the frequency of the light in hertz (Hz).
Using these steps, you should be able to calculate the wavelength and frequency of the light falling on the double-slit system.