Diffraction Patterns Question

[Quelsita]

OK, I'm working on a homework problem and I'm a little stuck.

Problem:
You want to detect th efringes in he diffraction pattern produced by sunlight passing through a fine slit in the blinds covering a window. You have available a filter that blocks all wavelengths except 550nm, and you place this filer over the slit.

a) Will you be able to detect diffraction fringes if the width of the slit is 0.1mm?
Tke into account that the Sun's angulr diameter is about 1/2deg.
b)Will you be able to detect fringes if the wdth of the slit is 0.01mm?
c)Will you be able to detect diffraction fringes if you remove the filter?

-Can you just use asin(theta)=lambda and plug in the information?
-for part c, this means to confirm if the fringes are visible at any wavelength other than 550nm?

Thanks!

 

[jbsteele]

Yes, you can use the formula sin(theta) = lambda to answer the questions. For part a), plug in the information given (1/2deg and 0.1mm) into the equation to determine the wavelength of the fringes. If the wavelength is 550nm, then you will be able to detect the diffraction fringes. For part b), plug in the information given (1/2deg and 0.01mm) into the equation to determine the wavelength of the fringes. If the wavelength is 550nm, then you will be able to detect the diffraction fringes. For part c), you will need to calculate the wavelength of the fringes for different slit widths and angles to determine if the diffraction fringes are visible at any wavelength other than 550nm.

 

[baba89]

Hello! Thank you for reaching out with your question. I am happy to provide some guidance and clarification on this homework problem.

First, let's review the concept of diffraction patterns. When light passes through a small opening, such as a slit, it spreads out and creates a pattern of bright and dark fringes. This is known as a diffraction pattern. The size of the opening and the wavelength of the light determine the spacing of these fringes.

Now, let's address the specific questions in the problem.

a) Yes, you should be able to detect diffraction fringes if the width of the slit is 0.1mm. This is because the Sun's angular diameter of 1/2 degree is relatively large compared to the width of the slit. However, the fringes may be faint and difficult to detect.

b) If the width of the slit is reduced to 0.01mm, the diffraction fringes will become more prominent and easier to detect. This is because the smaller slit size will lead to a larger spread of the light and therefore a wider spacing of the fringes.

c) If you remove the filter, you will still be able to detect diffraction fringes. However, the spacing of the fringes will be different since the filter was blocking all wavelengths except for 550nm. As you mentioned, you can use the equation asin(theta) = lambda to calculate the spacing of the fringes at different wavelengths. This means that the fringes will be visible at any wavelength, but the spacing will vary depending on the wavelength.

I hope this helps clarify the problem for you. Keep in mind that diffraction patterns can be affected by various factors, such as the size of the opening, the wavelength of the light, and the distance between the opening and the screen. I encourage you to continue exploring this concept and don't hesitate to reach out with any further questions. Good luck with your homework!