Two narrow slits are 0.25mm apart. The dark fringe of order 55 is 0.8 degrees from the central bright fringe. What is the wavelength of the light?
To find the wavelength of light, we can use Young's double-slit experiment formula. The formula is given as:
λ = (d * sinθ) / m
Where:
λ is the wavelength of light
d is the separation between the two slits
θ is the angle of the fringe from the central bright fringe
m is the order of the fringe
Given:
d = 0.25mm = 0.25 * 10^(-3) m (converting mm to meters)
θ = 0.8 degrees
m = 55
First, we need to convert the angle θ from degrees to radians. The conversion formula is:
θ_radians = θ * (π / 180)
Using this formula, we can find:
θ_radians = 0.8 * (π / 180)
Next, we can substitute the values into the formula to calculate the wavelength:
λ = (d * sinθ_radians) / m
λ = (0.25 * 10^(-3) * sin(0.8 * (π / 180))) / 55
Calculating this expression will give us the value of the wavelength (λ) of the light.