In Thomas Young experiment , why does the slit's radius smaller than the wave length of the light passing through it?
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If your referring to a photon of light, I don't see how the wave length has anything to do with it. Amplitude would seem to factor in more but not really. Slits don't have a radius.
Quantum mechanics ... act like a particle and a wave. Neither is really what is probably going on.... light goes in a straight line when not being pulled/pushed by some electromagnetic field.
in my curriculum .. it's written that the slit must be smaller than the wavelength\[\lambda\] of the light wave for diffraction to occur .. and when I checked Wikipedia ,, it was also the same
Huygens' Principle & Reflection/Refraction
The laws of reflection and refraction can both be derived from Huygens' principle. Click on the image to the right to view an image of Huygens' principle as it applies to refraction. See how points along the wave front are treated as sources along the surface of the refractive medium, at which point the overall wave bends based upon the new medium.
The effect of both reflection and refraction is to change the direction of the independent waves that are emitted by the point sources. The effects of performing the rigorous calculations obtains results that are identical to what is obtained from Newton's geometric optics (such as Snell's law of refraction), which was derived under a particle principle of light. (Although Newton's method is less elegant in its explanation of diffraction.)
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We want the two slits to behave like point sources of light, so the diffraction pattern is clear. For this reason, the slit width should be small and technically, it turns out this works best if the slit width is smaller than the wave length of the incident light.