How Do You Solve the Diffraction Intensity Problem with Different Units?

In summary, the conversation discusses a problem involving the intensity of light passing through a slit, with the given equation I = I_{0} [\frac{sin[\pi a(sin\theta)/\lambda]}{\pi a(sin\theta)/\lambda}]^{2}. The original attempt at a solution used the incorrect units for the wavelength, and also neglected to convert the argument of the outer sine function to radians. The correct width of the slit is 50.0 micrometers, and the wavelength should be converted to the same units.
  • #1
Precursor
222
0

Homework Statement



[PLAIN]http://img714.imageshack.us/img714/8205/65617184.jpg

Homework Equations



[tex]I = I_{0} [\frac{sin[\pi a(sin\theta)/\lambda]}{\pi a(sin\theta)/\lambda}]^{2}[/tex]

The Attempt at a Solution



Here is my attempt:

[tex]I = I_{0} [\frac{sin[\pi (50)(sin\1)/632]}{\pi (50)(sin1)/(632)}]^{2}[/tex]

[tex]I = 3.00*10^{-4} I_{0} [/tex]

However, this solution is not one of the options. Where did I go wrong? Is it the units?
 
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  • #2
What is the width of the slit?

ehild
 
  • #3
The width of the slit is 50.0 [itex]\mu m[/itex]
 
  • #4
Is your wavelength in nanometers or micrometers?
 
  • #5
Precursor said:
The width of the slit is 50.0 [itex]\mu m[/itex]

The width is measured in micrometers, but the wavelength is given in nanometers. Use the same units for both.

Do not forget that the argument of the outer sine function is in radians.

ehild
 

Related to How Do You Solve the Diffraction Intensity Problem with Different Units?

1. What is a diffraction intensity problem?

A diffraction intensity problem refers to a situation where the intensity of a diffracted wave is affected by various factors, such as the wavelength of the incident wave, the size and shape of the diffracting object, and the distance between the object and the detector. It is a common problem encountered in the study of diffraction phenomena.

2. How does the size of the diffracting object affect diffraction intensity?

The size of the diffracting object plays a crucial role in determining the intensity of the diffracted wave. As the size of the object increases, the amount of diffraction also increases, resulting in a higher intensity of the diffracted wave. However, if the object is too small, it may not produce a noticeable diffraction pattern.

3. Can the wavelength of the incident wave affect diffraction intensity?

Yes, the wavelength of the incident wave has a significant impact on the diffraction intensity. Generally, shorter wavelengths result in a higher intensity of diffraction, while longer wavelengths lead to lower diffraction intensity. This is because shorter wavelengths have a smaller diffraction angle, resulting in a more concentrated diffracted wave.

4. How does the distance between the object and the detector influence diffraction intensity?

The distance between the diffracting object and the detector also affects diffraction intensity. As the distance increases, the intensity of the diffracted wave decreases. This is because the diffracted wave spreads out over a larger area as it travels from the object to the detector, resulting in a lower intensity.

5. What are some techniques that can be used to minimize diffraction intensity problems?

There are several techniques that can be used to minimize diffraction intensity problems. These include using a smaller aperture (which reduces the amount of diffraction), increasing the distance between the object and the detector, and using a monochromatic light source to reduce the range of wavelengths present. Additionally, proper calibration and alignment of equipment can also help minimize diffraction intensity problems.

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