Intensity of Single Slit Diffraction Patterns
The intensity decreases as we go to successive maxima away from the centre, on either side. The width of the central maxima is twice that of the secondary maxima. If this experiment is performed in liquid other than air, the width of the diffraction maxima will decrease and becomes 1/μ times. With white light, the central maximum is white and the rest of the diffraction bands are coloured.
I = I0 [(sinβ/2) / (β/2)]2
Here, β/2= π a sin θ /λ. So, the formula can be rewritten as,
I = I0 [sin(π a sinθ/λ) / (πasinθ)/λ]2
where,
- θ is the angle
- I0 is the intensity at θ = 0 (the central maximum)
The value of the first minima is calculated by using the expression of wavelength.
It is known that, asinθ = λ
As sinθ ≈ tanθ, the value becomes,
a (y/D) = λ
y = λD/a
The width of the central maxima is given as w=2y.
w = 2λD/a
where,
- λ is the wavelength
- D is the diameter
- a is the slit width
If lens is placed close to the slit, then D = f and w = 2fλ/a. Here f is the focal length of the lens.
Problems on Diffraction – Class 12 Physics
The bending of light at the edges of an obstacle whose size is comparable to the wavelength of light is called diffraction. To put it another way, it is the spreading of waves when they go through or around a barrier. Diffraction of light, as it is used to describe light, occurs more explicitly when a light wave passes by a corner or via an opening or slit that is physically smaller than the wavelength of that light, if not even smaller. The ratio of the wavelength of the light to the opening size determines how much bending occurs. The bending will essentially be undetectable if the aperture is substantially greater than the light’s wavelength. However, if the two are of similar size or are equal in size, there is a noticeable degree of bending that can be observed with the unaided eye.
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