Calculating the Slitwidth of a Diffraction Gradient

[bmb2009]

Homework Statement

A set of narrow vertical slits is located a distance D from a screen. The slits are equally spaced and have the same width. The intensity pattern in the figure is observed when light from a laser passes through the slits, illuminating them uniformly. The screen is perpendicular to the direction of the light. Data: Distance to the screen = 2.95 m, Wavelength of light = 620 nm, distance between the central maximum and first order bright fringe is 1.6 cm. Distance between slits is 1.166E-4 m and number of slits is 3.

Homework Equations

The Attempt at a Solution

I've tried a lot of things and it seems that I need to know the distance between the central maximum and the first order minimum (the first dark fringe). The equations i thought were relevant were sinθ = λ/a where λ is wavelength and a is slit width, and tanθ= y/L where y is the distance from the central mxaimum to the first dark fringe and L is the distance to the screen. So i figured i need to solve for the angle with the second equation and then plug that into solve for the slit width but it doesn't seem to work. What am I doing wrong?
Thanks in advance!

 

[Delphi51]

It would be nice to know what the question is.

I need to know the distance between the central maximum and the first order minimum

That should be half of the distance between the central max and the first bright spot, 0.8 cm.

There is a lot of confusion between L and the perpendicular distance to the screen, but it usually doesn't matter. However, it should certainly be sin θ = y/L or else tan θ = y/2.95. Hard to say what went wrong in your calc when you don't show it. Note that any rounding of θ will strongly affect the value for a.

 

[bmb2009]

sorry i just realized some of the question didn't copy over... but i ended up figuring it out.. Thank you anyway!