## Introduction: Measure Wavelength of Laser Pointer.

Shinning a laser pointer thru a microscope calibration grid (0.1mm spacing), I was pleased to see an interference pattern projected on the opposing wall. In this instructable we will take some measurements and attempt to calculate the wavelength of my laser pointer.

## Supplies

Laser pointer - low power

Microscope Calibration Ruler or Diffraction Grating.

Tape measure

Camera

## Step 1: Setup the Experiment

Mount the diffraction grating (with known spacing) vertically some distance from a wall. Aim for sufficient distance so that the bright spots in the interference pattern are adequately separated. Grid spacing will increase with distance, but may become too dim to distinguish. Make sure your diffraction grating is parallel to the surface being projected to.

Mount a target of known dimensions on the wall, this will be the projection plane. I used a bright paper square measuring 98.2mm on each side.

Measure the distance from the grating to the projection plane. In my setup the distance was 649mm.

Shine the laser thru the grating so that a clear interference pattern is visible on the target. Capture an image of the target on a camera. (Hold the camera at the same height as the target so that you're not tilting the camera up or down, a sideway view is the only way to capture the image without blocking the light, but try to minimize this angle as much as possible.)

## Step 2: Measurements

Open your image in a Paint program.

We know the dimension of the target, use the paint program to measure the width of the target in pixels. For more accuracy measure at the same height as the bright spots.

In my case this was 818 pixels = 98.2mm

Then using the same method measure the distance in pixels between the centers of adjacent bright spots.

I got 37 pixels.

Now calculate the distance between the center of the bright spots.

37 is 22.108 times smaller than 818, the distance represented by 37 pixels is 22.108 times smaller than 98.2mm.

37pixels = 98.2mm/22.108 = **4.44mm**

## Step 3: What Are We Calculating?

The bright spots on the target result from constructive interference, or when the light waves arrive in phase. The dark spots in between are a result of destructive interference, or when the light waves are not in phase, 180° out of phase for the center of the dark spot.

Looking at the first bright spot directly behind the target, it is easy to see paths a and b are the same distance, so the light arrives in phase and we have constructive interference.

Now imagine a spot where the light meets that is moving towards the left of the image starting from the first bright spot, paths a and b will start to differ in length, until we get to where the dashed lines meet, this is the darkest spot. At this point path b is exactly half a wavelength longer than path a. the light waves arrive 180° out of phace.

If we continue moving left we reach the next bright spot. Here I called the paths c and d.. path d is exactly one wavelength longer than path c. If we can calculate the lengths of these paths and subtract them we would have calculated the wavelength of our laser pointer.

## Step 4: Pythagoras

**EDIT: I have made a silly mistake, the values in the figures above should be 4.39mm and 4.49mm.**

The spacing of the slits id 0.1mm, the first bright spot sits in the middle, 0.05mm.

One side of our triagle is 649mm as measured, the top side is 4.44mm - 0.05mm = 4.39mm

Using Pythagoras we know h1 is the square root on the sum of the other sides squared.

Likewise use geometry to calculate the sides of the triangle for h2.

giving us Lambda (wavelength) = sqrt(649^2 + 4.49^2) - sqrt(649^2 + 4.39^2)

## Step 5: Google It!

type

sqrt(649^2 + 4.49^2) - sqrt(649^2 + 4.39^2)

into Google and we get our answer 0.00068411341

but remember all our measurements were in mm, so we need to divide by 1000 again to get our answer in meters.

Then final answer is **684nm**

Which when compared to actual wavelengths , also Googled, sits nicely within the range for red light!.

## Step 6: Vary It Up

Repeat the experiment and try to calculate the missing parameter.

For example, setup the experiment an unknown distance form the target and try to calculate it.

Or use a grating with different spacing and try to calculate it from the other measurements. etc

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