Double slit problem, finding λ of second laser given data about first laser

In summary, the problem involves using a laser with a specific wavelength to create an interference pattern on a screen. A second laser with a different wavelength is then shone through the same slits, and the goal is to determine the wavelength of the second laser that would place its second maximum at the same location as the fourth minimum of the first laser. Equations are used to set the two wavelengths equal to each other, and the correct answer is found to be 9/2 times the wavelength of the first laser.
  • #1
aliaze1
174
1

Homework Statement



A laser with wavelength d/8 is shining light on a double slit with slit separation 0.500 rm mm. This results in an interference pattern on a screen a distance L away from the slits. We wish to shine a second laser, with a different wavelength, through the same slits.

What is the wavelength λ2 of the second laser that would place its second maximum at the same location as the fourth minimum of the first laser, if d = 0.500 mm?


Homework Equations



http://photo.ringo.com/233/233184793O806463150.jpg [Broken]

http://photo.ringo.com/233/233184793O806463150.jpg [Broken]

The Attempt at a Solution



I have only one attempt left, so I used those equations and made them both sin(θ)= ..., and set them equal to each other. I got an answer of 1/56 but I do not want to use it and loose my last attempt and get the problem wrong. can anybody confirm this?

Thanks
 
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  • #2
i should also add that i got 1/36, but it said that the first minimum corresponds to m=0 not m=1, would this also apply to the maximum? if so, that is how i got 1/56...
 
  • #3
Since the maxima and the minima are at the same point, [tex]dsin\theta[/tex] for both cases is the same.

For the first case, [tex]dsin\theta=2\lambda _1[/tex].

For the second case, [tex]dsin\theta=\frac{9}{2}\lambda _2[/tex] (m=4)

Equate the two and solve, your answer seems to be incorrect.
 

What is the double slit problem?

The double slit problem is a phenomenon in physics where a single beam of light is split into two beams as it passes through two parallel slits. This results in an interference pattern on a screen behind the slits, which is difficult to explain using classical wave theory.

How is the wavelength (λ) of a second laser determined using data from the first laser?

To determine the wavelength of a second laser using data from the first laser, the interference pattern created by the second laser must be compared to the pattern created by the first laser. By measuring the distance between the peaks of interference and knowing the distance between the two slits, the wavelength of the second laser can be calculated using the formula λ = d sinθ, where d is the distance between the slits and θ is the angle between the two beams.

Why is the double slit problem important in understanding the nature of light?

The double slit problem is important because it challenges the classical wave theory of light and points towards the wave-particle duality of light. It also helps us understand the fundamental properties of light and its behavior as both a wave and a particle.

What are some real-life applications of the double slit problem?

The double slit problem has various real-life applications, such as in the field of optics for creating diffraction gratings and in the development of technologies like holography. It also plays a crucial role in understanding the principles of quantum mechanics and has implications in fields like quantum computing and cryptography.

How can the double slit problem be further explored and studied?

The double slit problem is continuously being studied and explored through experiments and theoretical models. Scientists are also using advanced technologies like electron and neutron interferometry to further understand the phenomenon. Additionally, research is being conducted to explore the implications of the double slit problem in other areas of physics, such as quantum entanglement and superposition.

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