Angular Width Of Central Diffraction

In summary, the angular width of the central diffraction peak can be calculated using the equation Θ=arcsin(m*λ/d), where m=1, λ=350nm, and d=0.20mm. However, to avoid a mathematical error, the units for both λ and d must be the same, such as nm for λ and mm for d. Therefore, the value for d should be 0.20*10^-7 km.
  • #1
Chris18
12
0
350nm falls on a single slit of width of 0.20mm. What is the angular width of the central diffraction peak?
I think that the width should be equal to 2Θ, where Θ=arcsin(m*λ/d)... m=1 and we have λ=350*10^-9 and d= 0.20*10^-6...but when i do the calculations I get 1.75 and the arcsin is a maths error...Could anyone help me please?
 
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  • #2
Chris18 said:
λ=350*10^-9 and d= 0.20*10^-6
Are those numbers in the same unit?
 
  • #3
λ=nm and d= mm
 
  • #4
Note 1 mm ≠ 10-6 m.
 
  • #5
Ok so I must have 10^-7 ?
 
  • #6
Chris18 said:
d= 0.20*10^-6
You should have written the unit as well, if you write it correctly it will be ##d= 0.20 \times 10^{-6}## km. If you use km for d then you must also use km for ##\lambda##.
 

FAQ: Angular Width Of Central Diffraction

What is the angular width of central diffraction?

The angular width of central diffraction is a measure of the spread of light waves as they pass through an opening or aperture. It is typically measured in radians or degrees and represents the angle between the first dark fringe on either side of the central bright fringe.

How is the angular width of central diffraction calculated?

The angular width of central diffraction can be calculated using the equation θ = λ / d, where θ is the angular width, λ is the wavelength of the light, and d is the size of the aperture. This assumes that the aperture is circular and the light is monochromatic.

What factors affect the angular width of central diffraction?

The angular width of central diffraction is affected by the wavelength of the light, the size and shape of the aperture, and the distance between the aperture and the screen where the diffraction pattern is observed. It is also influenced by the properties of the light source and the medium through which the light travels.

What is the significance of the angular width of central diffraction?

The angular width of central diffraction is an important concept in the field of optics and is used to understand and predict the behavior of light waves as they pass through small openings. It also has practical applications in areas such as microscopy, astronomy, and digital imaging.

How does the angular width of central diffraction relate to other diffraction phenomena?

The angular width of central diffraction is closely related to other diffraction phenomena, such as the diffraction grating and the double-slit experiment. It helps to explain the interference patterns observed in these experiments and can be used to calculate the positions of the fringes. Additionally, the angular width of central diffraction can be used to determine the resolving power of optical instruments.

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