What is the effect on a diffraction pattern when reducing the width of the slit?

In summary, when a wide single slit is placed in front of a diffraction grating and its width is slowly reduced, the diffraction angle θ remains the same but the width of the mth order line, w, increases. This is because the number of grating-lines exposed is reduced, causing the diffraction pattern to become wider. This is represented by choice C.
  • #1
hidemi
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Homework Statement
The width of single slit slowly reduced. As a result?
Relevant Equations
a*sinθ = mλ
Monochromatic light is normally incident on a diffraction grating. The mth order line is at an angle of diffraction angle θ and has width w. A wide single slit is now placed in front of the grating and its width is then slowly reduced. As a result:
A. both θ and w increase
B. both θ and w decrease
C. θ remains the same and w increases
D. θ remains the same and w decreases
E. θ decreases and w increases

Ans: C
I think I can use the equation above but I don't know where to start.
Thanks
 
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  • #2
What is it that changes if a wide slit is placed in front of the grating ? Compare with here
 
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  • #3
BvU said:
What is it that changes if a wide slit is placed in front of the grating ? Compare with here
I saw your link, but I still cannot relate it to the question. Could you explain more clearly, please?
 
  • #4
That would be telling.
What does you relevant equation tell you about ##\theta## ?
In the (four!) pictures, what has a relation with w ? (hint: does not feature in your equation)
 
  • #5
BvU said:
That would be telling.
What does you relevant equation tell you about ##\theta## ?
In the (four!) pictures, what has a relation with w ? (hint: does not feature in your equation)
I still don't understand :(
 
  • #6
hidemi said:
I saw your link, but I still cannot relate it to the question. Could you explain more clearly, please?
@BvU's link is extremely useful if you read through all of it.

A simple optical diffraction grating has hundreds of 'lines' each mm. Each grating-line is basically a very narrow slit.

If you cover the grating with a 'wide single slit' you leave only a small number of grating-lines exposed, e.g. 50 lines. When you shine light at the grating, the diffraction pattern is produced by only 50 grating-lines.

If you reduce the width of the 'wide single slit', this reduces the number of grating-lines exposed, e.g. to 20 lines. When you shine light at the grating, the diffraction pattern is now produced by only 20 grating-lines.

Read through @BvU's link and see how the changing the number of lines affects the diffraction pattern.
 
  • #7
Again. Can you write the relationship between slit width w, wavelength ##\lambda## and diffraction order m?
 
  • #8
hidemi said:
I still don't understand :(
Does the wide slit appear in your relevant equation ?
 
  • #9
Steve4Physics said:
@BvU's link is extremely useful if you read through all of it.

A simple optical diffraction grating has hundreds of 'lines' each mm. Each grating-line is basically a very narrow slit.

If you cover the grating with a 'wide single slit' you leave only a small number of grating-lines exposed, e.g. 50 lines. When you shine light at the grating, the diffraction pattern is produced by only 50 grating-lines.

If you reduce the width of the 'wide single slit', this reduces the number of grating-lines exposed, e.g. to 20 lines. When you shine light at the grating, the diffraction pattern is now produced by only 20 grating-lines.

Read through @BvU's link and see how the changing the number of lines affects the diffraction pattern.
Thanks for explaining it!
However, your explanation sounds like D is the correct answer, instead of C. Could you explain further? Thank you
 
  • #10
hidemi said:
Thanks for explaining it!
However, your explanation sounds like D is the correct answer, instead of C. Could you explain further? Thank you
Look at @BvU's link: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/mulslid.html

Suppose a 'single wide slit' of width L is placed against a diffraction grating so 5 grating-lines of the diffraction grating are left exposed.. The diffraction image produced is shown by the bottom image in the link - the diagram labelled 'Five Slit Diffraction'.

Note there are five sharp 'maxima’ in the central region (the 0-th order line, two 1-st order lines and two 2nd order lines). Each maximum has width w, and w is quite small because the maximum is narrow.

Now reduce L so only 2 grating-lines on the diffraction grating are exposed. The diffraction image produced is shown on the diagram labelled 'Double Slit Diffraction'. You can easily see the five maxima are now wider but at the same angular positions. The value of ##\theta## for each maximum is unchanged but its width (w) has increased.

Reducing L leaves θ unchanged and increases w - exactly matching choice C.

The real challenge is to understand why changing the number of slits changes w. To do this you have to have a good understanding of how multiple slits produce a diffraction image.
 
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  • #11
Steve4Physics said:
Look at @BvU's link: http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/mulslid.html

Suppose a 'single wide slit' of width L is placed against a diffraction grating so 5 grating-lines of the diffraction grating are left exposed.. The diffraction image produced is shown by the bottom image in the link - the diagram labelled 'Five Slit Diffraction'.

Note there are five sharp 'maxima’ in the central region (the 0-th order line, two 1-st order lines and two 2nd order lines). Each maximum has width w, and w is quite small because the maximum is narrow.

Now reduce L so only 2 grating-lines on the diffraction grating are exposed. The diffraction image produced is shown on the diagram labelled 'Double Slit Diffraction'. You can easily see the five maxima are now wider but at the same angular positions. The value of ##\theta## for each maximum is unchanged but its width (w) has increased.

Reducing L leaves θ unchanged and increases w - exactly matching choice C.

The real challenge is to understand why changing the number of slits changes w. To do this you have to have a good understanding of how multiple slits produce a diffraction image.
Thank you so much for the explanation! I got it :)
 
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  • #12
The take away from a*sinθ = mλ or sinθ = mλ/a is:

small a ##\Rightarrow## big ##\theta##​
or: small features ##\Rightarrow## big pattern​

and conversely.

That's why the single grating slit envelope is a wide feature. and -- in this exercise -- the wide slit has an effect on the smaller w.

It will come back later in Fourier transforms, Heisenberg uncertainty, signal processing and what have you.

##\ ##
 

Related to What is the effect on a diffraction pattern when reducing the width of the slit?

1. What is diffraction?

Diffraction is a phenomenon that occurs when a wave, such as light or sound, encounters an obstacle or slit and bends around it, creating a pattern of interference.

2. How does the width of the slit affect the diffraction pattern?

The width of the slit directly affects the diffraction pattern by determining the amount of diffraction that occurs. A narrower slit will produce a wider diffraction pattern, while a wider slit will produce a narrower diffraction pattern.

3. What happens to the intensity of the diffraction pattern when the slit width is reduced?

When the slit width is reduced, the intensity of the diffraction pattern decreases. This is because a narrower slit allows less light to pass through, resulting in a weaker diffraction pattern.

4. How does the distance between the slit and the screen affect the diffraction pattern?

The distance between the slit and the screen affects the diffraction pattern by changing the angle at which the light waves diffract. As the distance increases, the diffraction pattern becomes wider and less intense.

5. What is the relationship between the wavelength of light and the diffraction pattern when the slit width is reduced?

The wavelength of light has a direct relationship with the diffraction pattern when the slit width is reduced. As the wavelength decreases, the diffraction pattern becomes wider. This is because shorter wavelengths are more easily diffracted by narrow slits.

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