# Basic Background Knowledge

In my project, I will try to measur the wavelength of the laser.

# Objectives

To measur the wavelenth of the laser light by using a steel rule as a diffraction grating.

# Apparatus

He-Ne Laser & Steel Rule

# Principles

Specular reflection of the laser beam from a steel ruler gives a zero order image. In Fig.1 the distance h0 and D determine ,the angle of reflection:=arctan(D/h0) and hence also , the angle of diffraction for the nth order is

Figure 1: Schematic of diffraction from ruler markings.

Let d be the separation of lines on the steel ruler. For the nth order, the path difference between waves from successive ruler lines is =AC-BE. But and .

Hence

Figure 2: Geometry required for constructive interference.

# Measurement & Results

Put the squared paper on the wall, put the steel rule on te horizontal desk. Open the laser light generator and let the laser irradiate on the separated lines on the steel rulers.

Fig.3 below shows the setup schematicly.

Figure 3: setup

The results are shown below:

# Data

D=66.8 cm

d=1/64 inch=0.03969 cm

Theta_i=arctan(66.8/3.71)=86.82

Delta_1=arctan(66.8/5.30)=85.46

Wavelength Lambda_1=6.33*E-5 cm =633nm

Delta_2=arctan(66.8/6.50)=84.44

Wavelength Lambda_1=6.28*E-5 cm =628nm

Delta_3=arctan(66.8/7.56)=83.54

Wavelength Lambda_1=6.36*E-5 cm =636nm

# The average value of wavelength is 632nm

Now we must pay attention to the measurement of the distance D between the wall and the steel ruler. The fig.4 below tell us that there is not a spot but a strip on the steel ruler when the laser irradiates on it.

Figure 4: Steel Ruler

So we choose the center of the strip as one terminal of the distance D.