Find Lambda_2 for Double Slit Interference Pattern

In summary, the problem involves determining the wavelength of a second laser that would produce an interference pattern with its second maximum at the same location as the fourth minimum of the first laser. This can be solved by setting two equations equal to each other and solving for lambda_2, with the final answer being (2/9)d.
  • #1
yo_man
12
0

Homework Statement


A laser with wavelength d/8 is shining light on a double slit with slit separation d. 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 (lambda_2) of the second laser that would place its second maximum at the same location as the fourth minimum of the first laser?
Express your answer in terms of d

Homework Equations


I have (dsin(theta)) = 2(lambda_1)
and dsin(theta)= (9/2)(lambda_2)


The Attempt at a Solution



I set the two equations equal to each other, and solve for lambda_2 and get (2/9)dsin(theta), but then it said the answer does not depend on theta.. so I just guessed and put (2/9)d and it said I was off by a multiplicative factor. basically, I'm confused and do not know how to go about solving this problem. please help!
 
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  • #2
I have (dsin(theta)) = 2(lambda_1)
and dsin(theta)= (9/2)(lambda_2)
Check this.
Second maximum of second laser and fourth minimum of the first laser
 
  • #3
is it

(2(lambda_2)L)/d = ((4+.5)(d/8)L)/d
 
  • #4
Yes.
 

1. What is the double slit interference pattern?

The double slit interference pattern is a phenomenon that occurs when a light wave passes through two narrow slits and creates a pattern of light and dark bands on a screen behind the slits. This pattern is caused by the interference of the light waves from each slit.

2. How is lambda_2 calculated for a double slit interference pattern?

Lambda_2, also known as the second order maximum, is calculated by dividing the wavelength of the light by the distance between the slits. This can be represented by the equation lambda_2 = λ/d, where lambda is the wavelength and d is the distance between the slits.

3. What is the significance of finding lambda_2 in a double slit interference pattern?

Finding lambda_2 allows us to determine the wavelength of the light being used in the experiment. This is important because it can help us understand the properties of the light source and how it behaves when passing through the double slits.

4. How does the distance between the slits affect the double slit interference pattern?

The distance between the slits has a direct impact on the interference pattern. As the distance increases, the interference pattern will become more spread out, resulting in wider and dimmer bands. Conversely, a smaller distance between the slits will result in a more closely spaced and brighter interference pattern.

5. Can lambda_2 be used to determine the width of the slits in a double slit interference pattern?

No, lambda_2 cannot be used to directly determine the width of the slits. However, it can be used in conjunction with other measurements and equations to calculate the width of the slits. This is known as the diffraction grating equation, which takes into account the wavelength, distance between the slits, and the angle of diffraction to calculate the slit width.

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