Light problem -- diffraction grating distance between adjacent bright fringes

In summary, a laser with a wavelength of 760 nm is directed at a diffraction grating of 1500 lines/cm. If the diffraction grating is located 1.5 m from the screen, the distance between adjacent bright fringes is approximately 1.71 x 10^-13 m.
  • #1
student07
36
1

Homework Statement


Light from a laser with a wavelength of 760 nm is directed at a diffraction grating of 1500 lines/cm. If the diffraction grating is located 1.5 m from the screen, calculate the distance between adjacent bright fringes.

Homework Equations


Δx = Lλ / d
760 nm = 7.60 x 10^-7 m = λ
1.5 = L
1cm/1500 = 6.67 x 10^-6 m = d

The Attempt at a Solution


Δx = (1.5 m)(7.60 x 10^-7 m) / (6.67x 10^-6 m) = 1.71 x 10^-13 m

I'm not sure if this is correct please help.
 
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  • #2
Can it be correct? You see the bright fringes on the screen. Their distances is in the range of mm or cm, Can 10-13 m true?
 
  • #3
ehild said:
Can it be correct? You see the bright fringes on the screen. Their distances is in the range of mm or cm, Can 10-13 m true?
I saw other people getting 1.72 cm which is 0.0172 m but the the answered I wrote is what I got in the calculator so I'm not sure how they got that
 
  • #4
You typed in wrong number in the calculator when you divided by 6.67x10-7.

I guess you did not use parentheses.
 
Last edited:
  • #5
Dear sudent,

you want to avoid this kind of disaster by estimating the outcome of a calculation before using an electronic calculator. In this case you divide 7.6 by 6.7 which is a little more than 1, and 10-7 by 10-6 which is 10-1.
Times 1.5 should give a little over 0.15. So your answer is 17.1 cm.
 
  • #6
BvU said:
Dear sudent,

you want to avoid this kind of disaster by estimating the outcome of a calculation before using an electronic calculator. In this case you divide 7.6 by 6.7 which is a little more than 1, and 10-7 by 10-6 which is 10-1.
Times 1.5 should give a little over 0.15. So your answer is 17.1 cm.
actually Ehild was right I did not use parenthesis when I divided by 6.67x10-7 so the actual answer is 0.171 m.

Thank you for your help guys!
 

1. What is a diffraction grating?

A diffraction grating is a device that consists of a large number of equally spaced parallel slits or grooves. When light passes through these slits, it is diffracted and produces a pattern of bright and dark fringes.

2. How is the distance between adjacent bright fringes calculated?

The distance between adjacent bright fringes, also known as the grating spacing, is calculated using the formula d = λ / sinθ, where d is the grating spacing, λ is the wavelength of light, and θ is the angle of diffraction.

3. What is the relationship between the grating spacing and the number of slits?

The grating spacing is directly proportional to the number of slits. This means that as the number of slits increases, the grating spacing also increases.

4. How does the distance between the light source and the diffraction grating affect the pattern of fringes?

The distance between the light source and the diffraction grating does not affect the pattern of fringes. However, it does affect the intensity of the fringes. As the distance increases, the intensity of the fringes decreases.

5. Can a diffraction grating be used to separate different wavelengths of light?

Yes, a diffraction grating can be used to separate different wavelengths of light. The grating spacing determines the angle at which each wavelength is diffracted, allowing for the separation of different wavelengths. This is known as spectral dispersion.

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