Homework Help: Dark Fringe Ratios Question

1. Oct 2, 2009

wilson_chem90

1. The problem statement, all variables and given/known data
Two different single slits are used in an experiment involving one source of monochromatic light. With slit 1 in place, the first dark fringe is observed at an angle of 45 degrees. With slit 2, the first dark fringe is observed at an angle of 55 degrees.

a) Which slit is widest? Why?
b) What is the ratio of the largest slit to the smallest?

2. Relevant equations

3. The attempt at a solution
a) Slit 1 would have the larger width length because once an angle increases the intensity of the maxima decreases. Since slit 1 has a smaller angle, it therefore has a larger width.

b) I'm onestly not sure how to get the ratio, simply because of the lack of information.. I'm not sure if i have to estimate the question or there's an actual full calculation. If anyone has suggestions, it would be greatly appreciated. Thanks

2. Oct 2, 2009

3. Oct 3, 2009

wilson_chem90

but im still lacking information though. I dont have wavelength or anything.

4. Oct 3, 2009

Delphi51

Just go ahead and try! You likely won't be able to find the slit width, but you may well get something like the ratio of slit width to wavelength for slit 1 and the same for slit 2. Then taking the ratio of them, the wavelength would cancel out and you'll have your answer.

5. Oct 3, 2009

wilson_chem90

ohhhh i get it. so basically im just setting them to eachother. Well what i did was i had wavelength 1/wavelength 2 = dsinO1/dsinO2, then i cancelled the wavelengths and got d2/d1 = sin02/sin01. Then i plugged the numbers in and got 0.81:0.71. Not sure if thats correct though.

6. Oct 3, 2009

Delphi51

According to the Wikipedia article, the single slit formula is
d*sin(A) = n*lambda
so you have d1*sin(45) = lambda
and d2*sin(55) = lambda
to work with. I think you have something upside down in your equation.

7. Oct 4, 2009

wilson_chem90

but don't you have to set them equal eachother, as in dividing them from one another? like d1/d2 = sin(45)/sin(55) ?

8. Oct 4, 2009

wilson_chem90

if i do all of the steps i get 0.41:0.71

9. Oct 4, 2009

Delphi51

Surely it is d1/d2 = sin(55)/sin(45).

10. Oct 4, 2009

wilson_chem90

i get the same answer as my original attempt if i do it that way

11. Oct 4, 2009

Delphi51

d1/d2 = sin(55)/sin(45) = 1.16 would be the final answer for (b).

12. Oct 5, 2009

wilson_chem90

yeah but thats not a ratio though... im supposed to find the ratio not a final answer right

13. Oct 5, 2009

Delphi51

Yes, it is the ratio of d1 to d2, the slit width in case 1 to the slit width in case 2.

14. Oct 5, 2009

wilson_chem90

so its 1.16 between the 2 slits?

15. Oct 5, 2009

Delphi51

Well, that's what I got. But you need to work it out yourself. I'm notorious for making mistakes in the arithmetic.