Lab 7 Interference and diffraction

Transcription

1 Prep this lab, as usual. You may paste this entire lab into your notebook, including the data tables. All this should be completed prior to the start of lab on Wednesday, and I will score your completed lab before you leave class that day. Physics Objectives: Lab 7 Interference and diffraction Use interference patterns to determine the spacing between two closely-spaced slits Use interference patterns to determine the thickness of a very thin object Use interference patterns to determine the spacing between two closely-spaced objects Introduction and relevant equations used: In this experiment, you will be recreating Thomas Young s 80 experiment in which he demonstrated the wave nature of light (the famed double-slit experiment. A collimated light source shines through a double slit with a center-to-center distance d (see diagram) and casts an interference pattern on the screen behind it at a distance L. For constructive interference, the path difference Δr = d sin θ = m λ, where m = 0,,, For small angles, sin θ tan θ, so d y m L = m λ. Rearranging, we get: y m = m λ L d for m = 0,,, y m is the location of the mth bright fringe, as measured away from the center point.

2 Alternatively, if we know the spacing of the slits d, the distance to the interference pattern from the slits L, and the distance from the center bright (also know as the zeroth order bright) to the first bright (st order bright), we could calculate the wavelength of the light source. In addition to double-slit interference, all waves can exhibit diffraction, the spreading of the wave as it passes through a small opening, around obstacles or past a sharp edge. In this lab you will look at several Fraunhofer diffraction patterns. Fraunhofer diffraction occurs when the rays passing through a narrow slit (or by an obstacle or edge) are approximately parallel to each other. This can be achieved experimentally by either placing the viewing screen far from the source of the diffraction (that s what you ll do) or by using a converging lens to focus the rays after they pass through the opening. You will measure the thickness of your hair with diffraction. When light hits a single obstacle (like a hair) it spreads out and forms a diffraction pattern on a distant screen that has its dark regions located by the equation a sin θ = m λ, where m = 0,,, where m identifies each interference minimum (the darkest spots between the bright spots): m = ±, ±, ±, ±,, and a is the thickness of your hair and θ is the angle to the m th minima as shown in the figure below. A diffraction grating is a piece of glass or plastic etched with a series of closelyspaced parallel lines, that acts like a prism. Usually, the spacing between the lines is stated on the grating, and this can be used to calculate the precise wavelength of a laser, which you will do. Equipment: For all parts of the lab, you will need goggles, a ringstand with clamp and a ruler. For all part of the lab, you will also need a helium-neon (He-Ne) laser, which has a fixed wavelength emission at 6.8 nm. Be careful where you are shining the laser. For Part, you will need a by 5 card and some tape. For Part, you will need a double-slit slide. For Part, you will need a diffraction grating slide. For Part, you will need a CD.

3 The sketch below shows the basic setup for Part, and you can substitute a doubleslit slide for Part or a diffraction grating slide for Part : screen m = m = y laser hair θ A plot of the light intensity versus position Central bright spot D Procedure Part Interference with a double-slit. Obtain a He-Ne laser, a double-slit slide, a ringstand with clamp and something to act as a screen.. Predict the distances from the center of the screen to the mth bright fringe for each of three slit separation distances.. Turn on the laser, and be sure to obtain an interference pattern on the screen. Make the measurements of the distances from the center of the screen to the mth bright fringe for each of three slit separation distances. Part Diffraction. Obtain a He-Ne laser, a by 5 card, a ringstand with clamp, and something to act as a screen.. Tape a hair across a large hole in a x 5 card. Shine the laser beam onto the hair and observe the pattern on the distant screen. From your measurements, calculate the thickness of your hair. Part A diffraction grating. Obtain a He-Ne laser, a diffraction grating slide, a ringstand with clamp, and something to act as a screen.

4 . Shine the laser beam at the slide and observe the pattern on the distant screen. From your measurements, calculate the distance between the grooves in the grating.. Choose a laser pointer and perform the same experiment. This time, though, determine the wavelength of the laser used. Part Determining the spacing of rows of grooves in a CD. Obtain a laser, a CD, and something to act as a screen.. Shine one of a laser of known wavelength onto a CD or DVD so that it hits the disc roughly tangent to a circle centered on the disc. You should see a diffraction pattern on the wall. When you see a nice pattern of dots on the wall, make measurements to calculate the distance between the rows of pits/bumps on the disc. The image below of a magnified CD should give you a calibration of the value you should find. Data Sketch the one of the interference patterns you see during this experiment.

5 Wavelength of He-Ne laser Distance to screen Table a Data from Part, interference, distance between slits Predicted location of bright fringe (mm) Actual location of bright fringe (mm) Table b Data from Part, interference, distance between slits Predicted location of bright fringe (mm) Actual location of bright fringe (mm)

6 Table c Data from Part, interference, distance between slits Predicted location of bright fringe (mm) Actual location of bright fringe (mm) Table Data from Part, diffraction Dark fringe Location of dark fringe (mm) Thickness of hair (mm)

7 Table a Data from Part, diffraction grating Published spacing between the lines Location of bright fringe (mm) Calculated spacing between the lines (mm) Table b Data from Part, diffraction grating Color of laser pointer used Location of bright fringe (mm) Calculated wavelength of laser pointer (nm)

8 Part Spacing of grooves on a CD Below, show the calculation and the final result of the spacing of grooves on a CD