Response:
1 slit width = 0.158 mm, slit separation = 0.633 mm, distance between diffraction maxima = 12.7 mm
Explanation:
This involves defining several terms:
λ, the wavelength of the beam
D, the distance from the plane to the slit
x, the distance between minima in the diffraction pattern (in single slit setups)
w, the fringe width for double slit setups
1. In a double slit experiment, the fringe width is also recognized as the distance between Maxima.
Thus, w=λD/d, leading to d=λD/w when rearranged.
So, d= (632.8 x 10^-9 x 1 x 10^3)/1
which equals d= 0.633mm.
For single slit diffraction, minima are defined by a*sinΘ= m*x
where a is the slit width and m is an integer.
For small angles, it simplifies to Θ= (x/D) = (λ/a), allowing us to solve for a:
a = λD/a
a = (632.8x10^-9 x 1)/4
yielding a= 0.158mm.
2. A grating with 20 slits/mm gives d= 1/20mm= 0.05x10^-3.
To find y (the distance between maxima), apply y= λL/d:
Finally, y= (632.8 x 10^-9 x 1)/0.05x10^-3, which results in y= 12.7mm.
