Find spacing between slits in a double slit experiement

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mkematt96
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Homework Statement


Online homework screenshot, problem 35 P.047: Young's double-slit question with 595 nm light at 2.65 degrees and 81% intensity, with an incorrect answer box showing 1.85e-06 m.


2. Homework Equations
I = Imax cos^2 ((2pi/lambda)dsin(theta))

.81Imax = Imax cos^2 ((2pi/lambda)dsin(theta))[/B]

To shorten up my work I divided out the Imax

3. The Attempt at a Solution

Not sure where I am going wrong. Is the 2.65 deg not the theta I am suppose to use? I divided out the I max, square rooted both sides, took the inverse cos of the left side to cancel out the cos on the right. Then proceeded to do the algebra.
Online homework screenshot, problem 35 P.047: Young's double-slit question with 595 nm light at 2.65 degrees and 81% intensity, with an incorrect answer box showing 1.85e-06 m.
Handwritten worked solution on lined paper: I = Imax cos^2((2pi/lambda) d sin theta), theta = 2.65 degrees, cos^-1(0.9) = (2pi d sin 2.65)/545nm, then d = 999 over a fraction with 2pi/545nm times sin(2.65), crossed out, and d = 25 over the same bracketed term, giving 0.0000529 m.
 
mkematt96 said:

Homework Equations


I = Imax cos^2 ((2pi/lambda)dsin(theta))[/B]
Check your notes or textbook to see if the factor of 2 (shown in red above) should be there.

Also, when doing the calculation think about whether or not the angle obtained from the cos-1 should be in radians or degrees.
 
That 2 shouldn't have been in my equation. I found the calculation of inv cos (.9) in radians instead of degrees. That then gave me the correct answer. Thanks for the help!