What is the Ratio of Slit Distance to Wavelength in Laser Diffraction?

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SUMMARY

The ratio of the distance between the slits (d) to the wavelength of the light (λ) in the laser diffraction problem is established as d/λ = 2.07. The first dark fringes occur at angles of ±14.0° from the original beam direction. The intensity equation I = I₀cos²(ø/2) and the phase difference ø = 2πdsinθ/λ are utilized to derive the angle Θ, which is calculated to be approximately 0.192 radians. The discussion highlights the importance of ensuring the correct unit of measurement, specifically radians, for the final answer.

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Homework Statement


After a laser beam passes through two thin parallel slits, the first completely dark fringes occur at ±14.0∘ with the original direction of the beam, as viewed on a screen far from the slits.

A)What is the ratio of the distance between the slits to the wavelength of the light illuminating the slits?
d/lambda = 2.07

B)What is the smallest positive angle, relative to the original direction of the laser beam, at which the intensity of the light is 110 the maximum intensity on the screen?

Θ=


Homework Equations



I = Iocos2(ø/2)

ø = 2∏dsinθ/λ


The Attempt at a Solution



so for this I solved for phi and then substituted that into the second equation and for this sinθ is ≈θ I just solved for theta in the 2nd equation

for ø= 2cos-1(√(1/10))
ø=2.498

then ø/(2∏(d/λ)) = Θ

for Θ I got .192 but I can't figure out what I did wrong

thank you in advance
 
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I'm getting the same as you.
Are you expected to give your answer in degrees or radiens?
 
radians is what we were told to do for all of these problems
 
What leads you to believe that you've done anything wrong then?
 

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