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Homework Statement
A grating has 1070 lines per centimetre, and a flat screen is perpendicular to the ray that makes the central peak of the diffraction pattern. The screen is 3.20 m from the grating. If light of two wavelengths, 630 nm and 705 nm, passes through the grating, what is the separation on the screen between the third-order maxima for the two wavelengths?
Homework Equations
mλ = dsinΘ
The Attempt at a Solution
d = 1/1070 = .000935 * 10 000 000 = 9345.79nm
λ1 = Θ1 = sin^-1(3*705 / 9345.79) = 13.0796°
λ2 = Θ2 = sin^-1(3*630 / 9345.79) = 11.6674°
[3.2tan(13.0796°)] - [3.2tan(11.6674)] = .082673 * 1000 = 82.67 nm
My answer is incorrect, can anyone see where I'm going wrong here?
Also, where I multiplied my numerator by 3 above, I did that due to the third order maxima, is that correct? I was impatient and also tried multiplying it by 2 instead, also incorrect.
Please help me out here.