Laser beam diameter after diffraction and single-slit wavelength

[Kawrae]

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...

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??

 

[christinono]

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...

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:

$$\lambda = (\frac{x}{L}) (\frac{d}{n-\frac{1}{2}})$$

 

[Kawrae]

I plugged in that formula and got a wavelength of 750 nm... which webassign is still saying is wrong...

Ack I am so confused!