Question

a) In double-slit interference experiment, path difference Δ = d sin θ. Use ray diagram and words to explain why bright spots located at where Δ = mλ and dark spots located at where Δ=(m+1/2)λ. Here m = 0, ±1, ±2, ±3, etc.

b)Use any resource you can find to study the single-slit diffraction. Explain how the diffraction pattern formed by laser light passing a single narrow slit with width w. Explain where the dark spots would located. (You should find the equation for this.) Use diagram(s) and words to explain why.

c) Explain what Babinet's principle is. Explain how you can measure the thickness of a hair using the principle of diffraction.

Answer 1

You can measure the width of a single hair. All you need is a dark room, a laser pointer, some cardboard, tape and a little bit of math. And, of course, someone’s hair.

1.       Make a frame that can hold your hair. I cut a square of cardboard about 15 centimeters (roughly six inches) wide, and then cut a small rectangle inside it. My inside cutout was about one centimeter (0.39 inches) wide and four centimeters (1.5 inches) tall.

2.       Take a human hair, maybe from your own head, or from a willing volunteer. Make sure it is long enough to tape at both ends of your inside rectangle. In my case, each hair had to be at least 5 centimeters long to make sure I could tape it at both ends.

3.       Tape the hair, as tight as you can, at the top and bottom of your frame, so that the hair runs through the middle of the inside cutout.

4.       In a dark room, stand more than a meter (more than three feet) away from a blank wall. Hold up the frame with your hair, and shine a laser pointer at the wall from just behind the hair, making sure it hits the hair along the way.

5.       You will see the light scatter to the sides as you hit the hair with your laser pointer.

Shine a laser pointer toward a wall, making sure it hits the hair on the way.

The hair is causing the laser’s light to diffract. Diffraction is the bending that takes place when a wave of light encounters an object, such as a human hair or a slit in a piece of paper. Light can act as a wave, and when it encounters the hair it splits into a regular pattern of lines. It will create a scatter pattern you can see on the wall. The size of the pattern from this diffraction is related to the size of the object that caused the scatter. This means that by measuring the size of your light scatter, you can — with a little math — figure out the width of your hair.

6.       Measure the distance from your hair to the wall where you are shining your pointer. It’s best to measure this in centimeters.

7.       Check the wavelength of light produced by your laser pointer. A red laser pointer will be about 650 nanometers and one issuing a green light will be about 532 nanometers. Usually this is listed on the laser pointer itself.

8.       Measure the light scatter on the wall. You want to measure the line from the center of the dot to the first major “dark” section. Also measure this in centimeters. It’s usually best to have a buddy, one person to hold the laser pointer and hair, the other to measure the pattern.