Help with Light Questions: Wavelength, Fringe, Diffraction

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The discussion revolves around two physics problems related to light, specifically concerning wavelength, diffraction, and fringe calculations. The first problem involves estimating the diameter of a laser beam at a distance of 16.0 km, where the user struggles with the calculations involving the aperture diameter and wavelength. The second problem focuses on finding the wavelength of light based on the position of a diffraction fringe and the dimensions of a slit, with the user expressing confusion about how to approach the calculations. Despite applying relevant formulas, the user reports that their answers are marked incorrect by the web platform. Clarification on the formulas and calculations is sought to resolve these issues.
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Light Questions - Please Help!

I thought I was doing this problem right, but according to webassign I'm not, and I can't figure out what I've done wrong... please help!

1. A helium-neon laser emits light that has a wavelength of 632.8 nm. The circular aperture through which the beam emerges has a diameter of 0.500 cm. Estimate the diameter of the beam 16.0 km from the laser.

>> Here's what I did:
min angle = d/L = .005/16000 = 3.125e-7
min angle = 1.22(lamda/D)
-> min angle/1.22 = lambda/D
3.125e-7/1.22 = 6.328e-7/D
-> 6.328e-7/2.56e-7 = D = 2.47

Not sure why this is wrong... :cry:

2. The second-order bright fringe in a single-slit diffraction pattern is 1.50 mm from the center of the central maximum. The screen is 80.0 cm from a slit of width 0.600 mm. Assuming that the incident light is monochromatic, calculate the light's approximate wavelength.

>> I'm not really sure how to start this at all. I know I'm looking for lambda and that a=6.0e-4m, L=0.800m, m=2

Any ideas??
 
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Kawrae said:
I thought I was doing this problem right, but according to webassign I'm not, and I can't figure out what I've done wrong... please help!

1. A helium-neon laser emits light that has a wavelength of 632.8 nm. The circular aperture through which the beam emerges has a diameter of 0.500 cm. Estimate the diameter of the beam 16.0 km from the laser.

>> Here's what I did:
min angle = d/L = .005/16000 = 3.125e-7
min angle = 1.22(lamda/D)
-> min angle/1.22 = lambda/D
3.125e-7/1.22 = 6.328e-7/D
-> 6.328e-7/2.56e-7 = D = 2.47

Not sure why this is wrong... :cry:

2. The second-order bright fringe in a single-slit diffraction pattern is 1.50 mm from the center of the central maximum. The screen is 80.0 cm from a slit of width 0.600 mm. Assuming that the incident light is monochromatic, calculate the light's approximate wavelength.

>> I'm not really sure how to start this at all. I know I'm looking for lambda and that a=6.0e-4m, L=0.800m, m=2

Any ideas??
For the second question, use this formula:

\lambda = (\frac{x}{L}) (\frac{d}{n-\frac{1}{2}})
 
I plugged in that formula and got a wavelength of 750 nm... which webassign is still saying is wrong...

Ack I am so confused! :eek:
 

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