Dark Fringe Ratios: Which Slit is Widest and What is the Ratio?

[wilson_chem90]

Homework Statement

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?

Homework Equations

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

 

[Delphi51]

You need a formula for the single slit interference pattern.
There is one at http://en.wikipedia.org/wiki/Single_slit#Single-slit_diffraction

 

[wilson_chem90]

but I am still lacking information though. I don't have wavelength or anything.

 

[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.

 

[wilson_chem90]

ohhhh i get it. so basically I am just setting them to each other. Well what i did was i had wavelength 1/wavelength 2 = dsinO1/dsinO2, then i canceled the wavelengths and got d2/d1 = sin02/sin01. Then i plugged the numbers in and got 0.81:0.71. Not sure if that's correct though.

 

[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.

 

[wilson_chem90]

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

 

[wilson_chem90]

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

 

[Delphi51]

like d1/d2 = sin(45)/sin(55) ?

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

 

[wilson_chem90]

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

 

[Delphi51]

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

 

[wilson_chem90]

yeah but that's not a ratio though... I am supposed to find the ratio not a final answer right

 

[Delphi51]

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

 

[wilson_chem90]

so its 1.16 between the 2 slits?

 

[Delphi51]

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