Light from a coherent monochromatic laser of wavelength λ=2.29e-4 m is incident on two slits, both of width a, separated by a distance d. The slits are placed a distance L away from a screen where L≫d and L≫a. The diffraction/interference intensity is plotted on the figure below as a function of sin(θ) (i.e. the X axis is sin(θ) where θ varies from −90∘ to +90∘).
If I know the difraction pattern (x-axix-> sin(theta); y-axix-> I/I0), how could I know the size of the slits (both are equal)?
sint=lambda/a
To determine the size of the slits (both equal), we can use the information provided in the diffraction pattern plot along with the given parameters.
In the diffraction pattern plot, the intensity is shown as a function of sin(θ), where θ is the angle of deflection from the central maximum. The central maximum corresponds to sin(θ) = 0, while the secondary maxima and minima occur at different values of sin(θ).
To find the size of the slits, we need to analyze the position and spacing of the secondary maxima in the diffraction pattern.
The spacing between the secondary maxima depends on the wavelength (λ) of the incident light, as well as the distance (L) between the slits and the screen. This spacing can be calculated using the formula:
d*sin(θ) = m*λ
where d is the distance between the slits, θ is the angle of deflection, m is the order of the maximum, and λ is the wavelength.
Since the slits are equidistant, the distance between adjacent maxima will be twice the distance between the slits (2a).
We can identify the positions of the secondary maxima in the diffraction pattern on the x-axis and determine the corresponding values of sin(θ). By substituting these values into the above equation, along with the known values of λ (2.29e-4 m) and L, we can solve for the distance between the slits (a).
Please note that measuring the size of the slits precisely from the diffraction pattern plot may be challenging due to various factors like the resolution of the plot and the accuracy of measurements. However, the general size of the slits can be estimated using this method.