Width of central maximum in a single slit diffraction pattern

[nawab pasha]

hi everybody.
I have a problem in finding the width of central maximum in a single slit diffraction pattern. theoritically, we say it is the distance between the two first minima on either sides of the central maxima. i feel this calculation leads to the width of central maxima+half minima on one side+half minima on other side.
please somebody help me.

 

[Claude Bile]

I usually take the width of a single-slit diffraction pattern to be the full-width at half-maximum of the central peak, because it nicely corresponds to the argument of the sinc^2 function the diffraction pattern represents.

In any case "width" of a single-slit diffraction pattern is somewhat arbitrary, and can really be whatever interval you define it to be. Astronomers I think use a different definition based on various criteria for resolving objects for example.

Claude.

 

[astrokreng]

Hello,

Thank you for your question. I can understand your confusion about the width of the central maximum in a single slit diffraction pattern. The theoretical calculation you mentioned is correct, but it is important to note that the width of the central maximum is not just the distance between the two first minima on either side.

In a single slit diffraction pattern, the central maximum is the peak in the intensity of the diffracted light. This peak is surrounded by smaller peaks known as secondary maxima and minima. The distance between the two first minima on either side of the central maximum is known as the angular width of the central maximum. However, the physical width of the central maximum is determined by the size of the slit and the wavelength of the light.

To calculate the physical width of the central maximum, you can use the formula w = λL/D, where w is the width of the central maximum, λ is the wavelength of the light, L is the distance from the slit to the screen, and D is the width of the slit. This formula takes into account the diffraction of light as it passes through the slit, resulting in a wider central maximum.

I hope this helps to clarify your confusion. If you need further assistance, please don't hesitate to ask. Best of luck with your research.