Experiment 30
Spectra and the Diffraction Grating

Objectives

To see the behavior of a diffraction grating and to use it to find accurate wavelength values for light from various sources.

Introduction

The diffraction grating behaves like a double slit, which is not surprising because it is composed of not two but many single slits.  The major difference in the light pattern produced by a grating is that the maxima (in intensity) are much sharper than those of a double slit.  The same equation,

1)         a sin Θ = nλ

describes both patterns where a is the difference between adjacent slits and n = 0, 1, 2 . . . is the order number of a particular fringe in the pattern.  If the light contains light of m different wavelengths, the first order (n=1) pattern will consist of two sets of m fringes symmetrically placed around the n=0 order fringe.  Each of the m fringes will be at a slightly different angle Θ with a characteristic color.

Procedure

Lay the meter stick on edge perpendicular to the light from your mercury (Hg) source.  Locate the grating a reproducible distance d from the meter stick and view the hole in the center of the meter stick.  Make d somewhere between 50 and 75 cm.  Align the source, hole and grating.  You will see 2 or 3 images on either side of the central image.  Turn the grating until the first order images appear to fall on the meter stick and are evenly spaced about the hole.  Measure to the nearest millimeter the distance from the central image to the first order image in all cases.  Calculate the spacing of the lines in the grating.  This is the value of a in equation 1.  Using this value of a, calculate the wavelength of light for each color in the Hg spectrum and compare with known values.  Hg sources may be contaminated with air so that you may see some lines (colors) due to the presence of nitrogen.

Repeat the above procedure for a hydrogen course and a HeNe laser.