How Does Wavelength Affect Double-Slit Interference Patterns?

[mar7pau]

Homework Statement

In a double-slit interference experiment, the slits are illuminated with a red laser light at 632 nm. The interference pattern seen on the screen is drawn below:
How would I carefully draw, in the same diagram, the pattern that you would see with a blue laser at 450 nm?

Homework Equations

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The Attempt at a Solution

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[ideasrule]

What are the equation giving the positions of the maxima and minima?

 

[tomcue]

I would first start by reviewing the basic principles of interference experiments and understanding the properties of light at different wavelengths. The interference pattern seen on the screen is a result of the interference between the two waves passing through the two slits. The distance between the slits and the wavelength of the light used determine the spacing of the fringes in the pattern.

To draw the pattern for a blue laser at 450 nm, I would need to consider the change in wavelength and how it affects the spacing of the fringes. As the blue laser has a shorter wavelength than the red laser, the fringes would be closer together. This means that the distance between the fringes would be reduced, resulting in a higher number of fringes in the same area. Additionally, the intensity of the fringes would also be affected, as the intensity of the fringes is directly proportional to the wavelength of the light.

To carefully draw the pattern, I would first mark the position of the central bright fringe, which is at the center of the screen. Then, I would carefully draw the fringes on either side, making sure that the spacing between them is smaller than that of the red laser pattern. The number of fringes on either side would also be higher. The intensity of the fringes would also be higher, with the central bright fringe being the brightest and the intensity decreasing towards the edges.

Overall, the interference pattern for a blue laser at 450 nm would be similar to the red laser pattern, with a higher number of fringes in a smaller area and a higher intensity. This demonstrates the relationship between wavelength and interference patterns, and how changing the wavelength can affect the interference pattern seen on the screen.