Find the angular width of the central maximum.

In summary, the conversation discusses finding the angular width of the central maximum of a single slit illuminated with light of a certain wavelength. The equation θ = λ / b is used, but the answer is slightly off, leading to a discussion about taking theta in radians and a helpful link provided by another member. The issue is resolved and the problem can now be solved accurately.
  • #1
bsmm11
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0

Homework Statement


A single slit of width 1.50 * 10-6m is illuminated with light of wavelength 500.0 nm. Find the angular width of the central maximum.

Homework Equations


θ = λ / b

The Attempt at a Solution


b = 1.50 * 10-6m
λ = 5.000 * 10-7
θ = λ / b = 0.333 = 19.1°

But the answer is 38.9°.

All my calculation of diffraction on single slit is off-target. It seems there is a fundamental point that I am missing. Please help. :frown:
 
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  • #2
You have found the angular position,measured from the centre,of the pattern.There are two such minima,one on each side of the central maxima.
 
Last edited:
  • #3
OK.. so what I need is 2Θ, right? Then I got 38.2, and this is a bit off from 38.9. Where did this difference come from?
 
  • #4
I calculated it to be 38.9.The equation is:
sin theta=lambda/d.
Did you take theta to be in radians?If so that is a good approximation but only for very small angles.
 
  • #5
I had a similar problem and was given this link.
http://www.calctool.org/CALC/phys/optics/fNA
It is a great link and solved my problem with units
 
  • #6
Now I can solve the problems. Thanks everyone! :D

p.s. Emily, the link is not valid. Could you give me a right one? I can solve the problems, but still I want to check it out.
 

FAQ: Find the angular width of the central maximum.

What is the central maximum?

The central maximum is the brightest and widest part of the diffraction pattern created when light passes through a narrow slit or aperture. It is located at the center of the pattern.

What is the angular width of the central maximum?

The angular width of the central maximum is the measure of the angle between the first dark fringe and the last bright fringe of the diffraction pattern. It is also known as the diffraction angle.

How is the angular width of the central maximum calculated?

The angular width of the central maximum can be calculated using the formula θ = λ / a, where θ is the diffraction angle, λ is the wavelength of the light, and a is the width of the aperture or slit. This formula is known as the diffraction grating equation.

What factors affect the angular width of the central maximum?

The angular width of the central maximum is affected by the wavelength of the light used, the width of the aperture or slit, and the distance between the source of light and the aperture. It also depends on the type of diffraction pattern, whether it is single-slit or double-slit.

Why is the angular width of the central maximum important?

The angular width of the central maximum is important because it affects the resolution and sharpness of the diffraction pattern. It also provides valuable information about the properties of the light source and the aperture used in the experiment.

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