Single slit diffraction pattern

[kevnm67]

Homework Statement

A single slit forms a diffraction pattern, with the first minimum at an angle of 40 from the central maximum. Monochromatic light of 410 nm wavelength is used. The same slit, illuminated by a different monochromatic light source, produces a diffraction pattern with the second minimum at a 60 angle from the central maximum. (Remember to convert degrees to radians – Recall: 2πrad=〖360〗^0.)
A) What is the width of the slit?
a. 587 nm b. 103 nm c. 1170 nm

B) What is the wavelength of the second light source?
a. 587 nm b. 307 nm c. 615 nm

C) If the screen is placed 1 meter away, what is the width of the central maximum for the 410 nm light source?
a. 0.70 m b. 1.4 m c. 2.

Homework Equations

w=2(λ)L/a

The Attempt at a Solution

a) I solved for "a" and got 7 x 10^-9 but don't know where to go from here?

 

[Doc Al]

a) I solved for "a" and got 7 x 10^-9 but don't know where to go from here?

Show how you got that answer.

Did you copy the problem correctly? I don't see any of the answer choices as being correct.

 

[kevnm67]

Show how you got that answer.

Did you copy the problem correctly? I don't see any of the answer choices as being correct.

Yep, it's copied correctly...

for a I did:

theta = p (lamda/a)
and I get 10.25, not the other no., I used the wrong angle.

 

[Doc Al]

Yep, it's copied correctly...

for a I did:

theta = p (lamda/a)

Ah... that formula is only an approximation. It's only true in the small angle limit, where sin(theta) ≈ theta, where theta is in radians. (I wondered why they mentioned radians!)

Using that approximation, I can see how they get their answers.

and I get 10.25, not the other no., I used the wrong angle.

Redo this calculation. In using the formula, make sure you convert the angle to radians.

 

[kevnm67]

Ok. I got it all now...radians! Thanks again, Dr. Al, ill be sure to give you credit on my final tomorrow ;)