Testing theory of diffraction

In summary, the angle to the first order maximum of the blue light is not consistent with the theory, but may be able to be solved by more careful measurement of the picture.
  • #1
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Homework Statement


A diffraction grating with 500 lines per mm is held directly in front of the lens of a digital camera, with a bright white light source 8m away. The image recorded by the camera shows both the light source and the spectrum created by the light source. We know that the CMOS array of the camera has a pitch of 0.0036 mm per pixel, and the separation between the light source in the image and the middle of the "blue" region in the spectrum is about 730 pixels, which translates to a distance of 2.63mm. Based on this information, find the angle to the first order maximum of the blue light. Does this angle agree with the theory?


Homework Equations


d*sin(θ)=λ
d = (1/500)mm
λ = 475 nm (for blue light)

The Attempt at a Solution


Using
d*sin(θ)=λ
This gives a prediction of about 13 degrees for θ.
I'm not even sure what the relevant distances would be to get an angle from the picture. I've tried many permutations, and the closest I can get to 13 degrees is just 3 degrees. Does anyone have any idea how I can test the equation by using the picture?
 
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  • #2
Here is the picture, by the way.
 

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  • #3
After thinking about this some more, I may have a lead on how to solve it. Some information I left out that I'm thinking is probably important is that the camera lens/objective has a focal length of 6.5 mm. I then used the simple lens equation to find the image distance (assumed object distance was infinity), which is 6.5 mm. Then, calculating magnification, M = -(si/so), and li = (si/so)*lo, where so is distance from lens to object, si is distance from lens to image, li is length in image plane, lo is length in "object plane". Then, using so = 8m, si = 6.5mm, li = 2.63mm, I find lo = 3.24 m. Then, using arc length s = r(theta), with s = 3.24 m and r = 8 m, I find theta = 23 degrees. Still a ways off, but I didn't measure the distance from the lens to the light source very carefully.
 
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1. What is the theory of diffraction?

The theory of diffraction describes how waves, such as light or sound, interact with obstacles or openings in a medium. It explains how the waves bend, spread, and interfere with each other in the presence of obstacles, leading to the phenomenon of diffraction.

2. How is the theory of diffraction tested?

The theory of diffraction can be tested through experiments using different types of waves, such as light or sound. These experiments involve creating obstacles or openings in a medium and observing the behavior of the waves as they pass through. The results of these experiments can be compared to the predictions of the theory to verify its accuracy.

3. What is the significance of testing the theory of diffraction?

Testing the theory of diffraction helps us understand and predict the behavior of waves in various situations. This knowledge is crucial in fields such as optics, acoustics, and radio frequency technology. It also allows us to develop and improve technologies that rely on diffraction, such as telescopes and ultrasound machines.

4. What are some applications of the theory of diffraction?

The theory of diffraction has numerous applications in different fields. In optics, it explains the phenomenon of light diffraction, which is used in the design of optical devices such as lenses and mirrors. In acoustics, it is used to understand the behavior of sound waves in different environments. The theory also has applications in radio frequency technology, such as designing antennas for better signal reception.

5. Are there any limitations to the theory of diffraction?

While the theory of diffraction is widely used and accepted, it does have some limitations. For example, it does not take into account the effects of polarization and coherence of waves, which can impact their behavior in certain situations. Additionally, the theory is based on idealized conditions and may not accurately predict the behavior of waves in real-world scenarios. Therefore, it is important to consider these limitations when applying the theory to practical situations.

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