How Wide Is the Slit in a Diffraction Experiment with 450nm Light?

In summary, the purpose of calculating the slit width is to determine the appropriate size of a narrow opening for light or particles to pass through. Factors such as wavelength, distance, and material affect the calculation, which is typically done using the equation w = λD/d. The slit width directly impacts the diffraction pattern, with a wider slit producing a broader pattern and a narrower slit producing a sharper one. However, there are limitations to the calculation due to idealized conditions and real-world factors.
  • #1
cassey
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Homework Statement


When 450nm light falls on a slit, the central diffraction peak (central maxima) on a screen 2.0m away is 6cm wide. Calculate the slit width?
wavelength= 450 x 10^9m
L= 2m
y= 0.06m
w=?

Homework Equations


y/L = tantheta = sintheta
sintheta = (m+1/2)lambda / w

The Attempt at a Solution


I attempted at this, and got this answer... can anyone check to see if I did it right?
y/L = sintheta
0.06/2 = 0.03

sintheta = (m+1/2)lambda / w
0.03 = (1+1/2) (450 x 10^-9) / w
w= 2.25 x 10^-5m
 
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  • #2
cassey said:
sintheta = (m+1/2)lambda / w
You are using a wrong formula. It should be ##\sin\theta = m\lambda / w##.
 
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What is the purpose of calculating the slit width?

The purpose of calculating the slit width is to determine the appropriate size of a narrow opening through which light or particles can pass. This is important in various fields such as physics, optics, and engineering, as it affects the diffraction and interference patterns of waves passing through the slit.

What factors affect the calculation of the slit width?

The factors that affect the calculation of the slit width include the wavelength of the light or particles passing through the slit, the distance between the source and the slit, and the distance between the slit and the screen or detector. Other factors such as the material and shape of the slit may also play a role.

How is the slit width calculated?

The slit width is typically calculated using the equation w = λD/d, where w is the slit width, λ is the wavelength of the light or particles, D is the distance between the source and the slit, and d is the distance between the slit and the screen or detector. This equation is based on the principles of diffraction and interference.

What is the relationship between the slit width and the diffraction pattern?

The slit width directly affects the width and intensity of the diffraction pattern produced by light or particles passing through the slit. A wider slit will result in a broader diffraction pattern, while a narrower slit will produce a sharper pattern. Additionally, as the slit width decreases, the intensity of the diffraction pattern increases.

Are there any limitations to the calculation of the slit width?

There are limitations to the calculation of the slit width, as it is based on idealized conditions and assumptions. In reality, factors such as imperfections in the slit, the presence of multiple slits, and the properties of the source and detector may affect the actual width of the diffraction pattern. Therefore, the calculated slit width should be considered as an estimate and may require adjustments in real-world scenarios.

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