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
http://hyperphysics.phy-astr.gsu.edu/Hbase/phyopt/slits.html
To find the wavelength and frequency of the light, we can use the double-slit interference equation:
Δy = (λ * L) / d
where:
Δy is the fringe separation on the screen,
λ is the wavelength of the light,
L is the distance from the double slits to the screen, and
d is the separation between the slits.
Given:
L = 4.60 m
d = 0.050 mm = 0.050 * 10^(-3) m
Δy = 5.7 cm = 5.7 * 10^(-2) m
Rearranging the equation, we can solve for λ (wavelength):
λ = (Δy * d) / L
Substituting the given values:
λ = (5.7 * 10^(-2) m * 0.050 * 10^(-3) m) / 4.60 m
Calculating this expression:
λ ≈ 6.1967 * 10^(-7) m
To convert the wavelength to nanometers (nm):
λ (nm) = λ * 10^9 nm/m
Substituting the calculated value of λ:
λ (nm) ≈ 6.1967 * 10^(-7) m * 10^9 nm/m
Calculating this expression:
λ ≈ 619.67 nm
Therefore, the wavelength of the light is approximately 619.67 nm.
To find the frequency (f):
We can use the equation:
v = f * λ
where:
v is the speed of light, which is approximately 3 x 10^8 m/s.
Rearranging this equation to solve for f:
f = v / λ
Substituting the values:
f = (3 x 10^8 m/s) / (6.1967 * 10^(-7) m)
Calculating this expression:
f ≈ 4.84 x 10^14 Hz
Therefore, the frequency of the light is approximately 4.84 x 10^14 Hz.