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

problems.proof.prevStep problems.proof.nextStep

|m|\lambda\le d\quad\Rightarrow\quad |m|\le3

problems.proof.analysis

A real direction requires $|\sin\theta_m|\le1$ . The grating equation therefore bounds the order magnitude by $d/\lambda$ .