Help with single slit diffraction (fraunhoffer)

[j-lee00]

urgent Help with single slit diffraction (fraunhoffer)

why is it a minimum at a*sin ($$\theta$$) = m*$$\lambda$$,

a = slit separation I would have thought if the path difference is equal to a whole wavelength then there would be constructive interference??

See http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

 

[Doc Al]

Don't confuse the double slit interference condition (http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/slits.html#c1").

In the single slit condition, when the light from opposite ends of the slit have a full wavelength phase difference, that means that half the light from the slit is exactly one half wavelength out of phase with the other half. Which mean destructive interference.

 

[astrokreng]

for a visual representation of single slit diffraction.Dear student,

Thank you for reaching out for help with single slit diffraction. I understand that you are confused about why there is a minimum at a*sin (\theta) = m*\lambda, even though you would expect constructive interference when the path difference is equal to a whole wavelength.

First, let me clarify that the equation a*sin (\theta) = m*\lambda is known as the diffraction condition for a single slit, and it is derived from the Fraunhofer diffraction equation. This equation describes the pattern of light that is diffracted by a single slit, and it is based on the principles of wave interference.

Now, to answer your question, it is important to understand that the diffraction pattern produced by a single slit is a result of both constructive and destructive interference. When the path difference is equal to a whole wavelength, constructive interference occurs at that particular point and a bright fringe is observed. However, at the same time, destructive interference is also occurring at other points along the diffraction pattern, resulting in dark fringes.

The diffraction pattern is a result of the interference of waves that are diffracted at different angles from different points along the slit. The equation a*sin (\theta) = m*\lambda represents the condition for constructive interference at a specific angle (\theta) and order (m). This means that at that particular angle and order, the waves diffracted from different points along the slit will have a path difference that is equal to a whole wavelength, resulting in constructive interference. However, at other angles and orders, the path difference will not be equal to a whole wavelength, leading to destructive interference and the formation of dark fringes.

I hope this explanation helps clarify why there is a minimum at a*sin (\theta) = m*\lambda in the diffraction pattern of a single slit. If you have any further questions, please do not hesitate to ask.

Best regards,