Problem 3

Monochromatic light of wavelength

\lambda

is incident normally on a transmission grating of spacing

d=3\lambda

with many narrow parallel slits per unit length. Neglect absorption and consider principal maxima; angle

\theta

is measured from the straight-through direction. (a) State the maximum condition and find the first-order angle. (b) List all observable orders and the largest order. (c) For a screen a distance

L

from the grating, find the transverse position

y_1

of the first-order maximum using exact geometry.

problems.proof.stepOf

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\tan\theta_1=\frac{y_1}{L}\quad\Rightarrow\quad y_1=L\tan(\arcsin\tfrac13)=\frac{L}{2\sqrt2}

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Screen geometry gives $y_1/L=\tan\theta_1$ . Since $\sin\theta_1=1/3$ , the positive cosine is $2\sqrt2/3$ , giving the stated tangent.