Diffraction grating problem

  • Thread starter scorpa
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  • #1
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Hello everyone,

My physics teacher assigned a whole bunch of homework that no one remembers how to do because we haven't taken light for a year and a half. I have gone through all of my old stuff but can't find the right unit, and what I did find isn't in enough detail. I am getting really frustrated with this so hopefully some of you guys can help me out.

1) In a double slit experiment a student used a diffraction grating in which the slit separation was 1.00x10^-4m. A screen was placed at a distance of 4.00x10^-1m from the grating. The student measured the distance from the central maximum to the 2nd order minimum and found it to be 3.00 x 10^-3m. What was the frequency of the light used by the student?

Answer ---> 6.00 x 10^14 Hz

2) Calculate the frequency of monochromatic light used in a diffraction experiment if the 1st order maximimum is observed at an angle of deviation of 28 degrees when the slits of the diffraction grating are 1.00x10^-6m apart.

6.39 x 10^14 Hz

3) Light with a frequency of 4.28 x 10^14 Hz is diffracted by a diffraction grating ruled 5.00 x 10^5 lines/m. On a screen 2.00m from the grating maxima are 7.00 x 10^-1m apart. What is the distance between maxima if the frequency of the light was increased 1.50 times while all other variable remain constant?

Answer ---> 4.66 x 10^-1 m
 

Answers and Replies

  • #2
353
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Ok I finally figured out the last two on my own, but I am still having a lot of trouble with the first one. I think I need to find the wavelength for it and then use the wavelength and the speed of light to find the frequency but nothing will work out for me.
 
  • #3
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Your intuition for part 1 was correct.

First find the wavelength of light using the double slit equation.

[tex]\lambda=\frac{dy}{mL}[/tex]

where d is the separation between the slits
y is the distance from the centre line
m is the order number
L is the distance between the grating and the screen

then continue on with your thought process and find the frequency using:

[tex]f=\frac{c}{\lambda}[/tex]
 
  • #4
Ouabache
Science Advisor
Homework Helper
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Bross7's equations are correct. You may keep units in meters.
I also tried your data and did not arrive at the solution you gave.
(It did come out to the same magnitude though; ie 10^14 Hz).

You may want to double check and see if your given data is correct.
If so, then the expected solution you gave is very likely, incorrect.
 
  • #5
xanthym
Science Advisor
410
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Ouabache said:
Bross7's equations are correct. You may keep units in meters.
I also tried your data and did not arrive at the solution you gave.
(It did come out to the same magnitude though; ie 10^14 Hz).

You may want to double check and see if your given data is correct.
If so, then the expected solution you gave is very likely, incorrect.

bross7 said:
First find the wavelength of light using the double slit equation.

λ = d*y/(m*L)

where d is the separation between the slits
y is the distance from the centre line
m is the order number
L is the distance between the grating and the screen

then continue on with your thought process and find the frequency using:

f = c/λ

1) In a double slit experiment a student used a diffraction grating in which the slit separation was 1.00x10^-4m. A screen was placed at a distance of 4.00x10^-1m from the grating. The student measured the distance from the central maximum to the 2nd order minimum and found it to be 3.00 x 10^-3m. What was the frequency of the light used by the student?

Answer ---> 6.00 x 10^14 Hz

The textbook's answer is CORRECT. Remember that the "2nd Order Minimum" occurs at m=(1.5). Using that value will result in the given answer.


~~
 

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