# Width of central maximum in a single slit diffraction pattern

• nawab pasha
In summary, the conversation discusses the calculation of the width of the central maximum in a single slit diffraction pattern. The theorized method involves finding the distance between the two first minima on either side of the central maximum, but the speaker suggests that this may lead to an incorrect measurement. They propose using the full-width at half-maximum of the central peak instead, as it aligns with the mathematical representation of the pattern. However, the width of a single-slit diffraction pattern is subjective and can vary based on different criteria.
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.

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.

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.

## What is the width of central maximum in a single slit diffraction pattern?

The width of the central maximum in a single slit diffraction pattern is dependent on the wavelength of the light source and the size of the slit. It can be calculated using the equation w = λL/d, where w is the width, λ is the wavelength, L is the distance from the slit to the screen, and d is the width of the slit.

## How does the width of the slit affect the width of the central maximum?

The width of the slit has a direct impact on the width of the central maximum. As the slit gets narrower, the central maximum becomes wider. This is because a narrower slit allows more diffraction to occur, resulting in a broader diffraction pattern.

## What happens to the width of the central maximum as the distance from the slit to the screen increases?

As the distance from the slit to the screen increases, the width of the central maximum decreases. This is because the diffraction pattern spreads out as it travels further, resulting in a narrower central maximum. However, the overall intensity of the pattern decreases as well.

## How does the wavelength of the light source affect the width of the central maximum?

The wavelength of the light source also plays a role in determining the width of the central maximum. As the wavelength increases, the width of the central maximum decreases. This is because longer wavelengths diffract less, resulting in a narrower diffraction pattern.

## Can the width of the central maximum be altered by changing the position of the slit?

No, the position of the slit does not affect the width of the central maximum. It only affects the overall intensity of the diffraction pattern. The width of the central maximum is solely determined by the wavelength of the light source and the size of the slit.

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