Pretend that you have a laser that is a combination of four different wavelength

Question

Pretend that you have a laser that is a combination of four different wavelengths of light at

= 656.3nm, = 486.1nm, = 434.1nm and = 410.2nm. You direct this laser light on a double slit with a slit width of a = 0.01mm and slit spacing of d = 0.03mm and view the resultant diffraction pattern on a screen 2.00m from the grating.

(a) Find the distances y1, , y1, , y1, and y1, to the first order (i.e. m = 1) diffraction
peaks for each of the four wavelengths.

(b) To what precision must we measure to resolve all four first-order maxima?

Explanation / Answer

d sin(theta) = m

d y / D = 1

y = D / d

(a)  y1, = 656.3 x 10^-9 x 2 / (0.03 x 10^-3) = 0.04375 m

  y1, = 486.1 x 10^-9 x 2 / (0.03 x 10^-3) = 0.0324 m

  y1, = 434.1 x 10^-9 x 2 / (0.03 x 10^-3) = 0.02894 m

y1, = 410.2 x 10^-9 x 2 / (0.03 x 10^-3) = 0.02734 m

(b) Precision up to 0.001 m = 1 mm

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