Two wavelengths, max/min at same angle

In summary, Based on the given information, we can conclude that for light with a wavelength of 440nm and 660nm passing through two slits 40 nm apart, there exists an angle at which the light with a wavelength of 440nm will have a maximum and the light with a wavelength of 660nm will have a minimum. The equation dsin\theta=m\lambda1 = maximum and dsin\theta=(m+ 1/2)\lambda2 = minimum can be used to solve for the integer values of m for each wavelength. It is important to note that the given distance between the two slits may have been a typo, as 40 mm is a large distance for an optical double slit setup and
  • #1
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Homework Statement


Light goes through two slits 40 mm apart. Does an angle exist at which light of wavelength 440nm has a maximum and light of wavelength 660nm has a minimum?

Homework Equations


dsin[tex]\theta[/tex]=m[tex]\lambda[/tex]1 = maximum
dsin[tex]\theta[/tex]=(m+ 1/2)[tex]\lambda[/tex]2 = minimum

The Attempt at a Solution


I solved for sin[tex]\theta[/tex] in each case, so I got:

m[tex]\lambda[/tex]1 = (m+ 1/2)[tex]\lambda[/tex]2

[tex]\lambda[/tex]1 = 660nm
[tex]\lambda[/tex]=440 nm

Now I'm stuck. Both Ms do not have to be the same, right? So do I have to solve for one of the Ms and stick it into an equation I listed in part 2 above? If so, that's a crazy calculation. Thanks!
 
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  • #2
Correct, the m's can be different. But they must both be integers.

Are the slits really 40 mm apart? That's pretty far for an optical double slit setup.
 
  • #3
They're actually 40 nm apart, sorry.
 
  • #4
Are you sure it's not 40 μm?
 
  • #5
ah yes you're right
 

What is the concept of two wavelengths, max/min at same angle?

The concept of two wavelengths, max/min at same angle refers to the phenomenon where two different wavelengths of light intersect at the same angle and result in either a maximum or minimum intensity of light. This can occur when two different waves of light superimpose on each other, creating an interference pattern.

What is the importance of understanding this concept?

Understanding this concept is important in various fields such as optics, physics, and astronomy. It helps in understanding the behavior of light and how it interacts with different materials and objects. It is also crucial in the development of technologies such as lasers and optical devices.

How is this concept observed in nature?

This concept can be observed in various natural phenomena such as the rainbow, where sunlight is refracted and dispersed into different wavelengths, resulting in a spectrum of colors. It can also be observed in thin film interference, where light is reflected and transmitted through different layers of materials.

What factors affect the max/min wavelengths at the same angle?

The max/min wavelengths at the same angle are affected by the properties of the materials the light is passing through, such as their refractive index and thickness. The angle of incidence and the polarization of the light also play a role in determining the interference pattern.

How is this concept used in practical applications?

This concept is used in various practical applications such as optical filters, which use interference patterns to selectively transmit or block specific wavelengths of light. It is also used in spectrophotometry, a technique for measuring the intensity of light at different wavelengths, which is used in chemical analysis and research.

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