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ISP 209L Lab 5: Optical Interference

Objectives

(A) To observe light transmitted through a very narrow slits and verify the relationship between the slit width and angles of the transmitted light. (B) To use the properties of light to measure the diameter of a small wire accurately by Babinet's Principle. (C) ) To observe light transmitted through two very narrow slits and to verify the relationship between the slit spacing and the angular separation of the transmitted light for the principle peaks.

Part A: Single-Slit Diffraction

Discussion

This week’s and next week’s exercises show that light acts like a wave. Essentially a wave phenomenon known as interference will creating symmetric and rather beautiful patterns. All of matter has a dual nature, acting like both particles and waves. For example, a particle of light (known as a photon) acts like a particle when in collides with an electron. However, that same particle will act like a wave if it is allowed to interfere with other photons, or even with itself.
This dual nature is described by Quantum Mechanics. However, the idea of combined particle and wave nature arose well before the development of Quantum Mechanics in the study of light. Newton argued that light must be particles because it did not appear to diffract and create interference patterns like other waves. Much later, Thomas Young demonstrated that light did diffract. This was one of the first indicators that the strict separation of particles and waves of classical physics was mistaken.

If a plane wave passes through a slit, the slit can be modeled as tiny sources of new waves, all in phase with each other. These sources spread out in all directions. Straight ahead, they all remain in phase and combine for a high intensity. To the sides, the intensity of the wave drops as only some of these wave sources can combine in phase. Eventually, there is no intensity because the sources are all out of phase and the amplitude of the sum is zero.

In the case of light, the relation between the wavelength λ of the light, the slit width, and the angle of observation where the intensity of light first becomes zero is:

λ = w x sin θ (1)

where w is the width of the slit. The geometry is shown in Fig. 1. L is the distance between the slit opening and the center of the screen; s is the distance between the central maximum and the first

minimum. For small angles, sin θ ( s/L, and Eq. 1 becomes

λ = ws /L . (2)

Suppose you measured s and L and the wavelength of the light is known. We could then use Equation (2) to find the slit width by rewriting it as:

w = λ L /s . (3)

[pic]

Figure 1: Geometry for the measurement (top view).

[pic]

Figure 2: Diagram of the optical bench (side view).

Part A: Setup and Data Taking Procedure / Questions

SAFETY NOTE: Do not stare directly into the laser beam. If laser light happens to flash into your eye, just move your head away.

Set up your laser on the lab bench so that it points away from the center of the room. The diagram of the apparatus is sketched in Fig. 2.

There are four narrow slits carved out of a thin aluminum foil which is mounted in a slide frame. The slits are labeled by their approximate width, i.e. 0.02mm, 0.04mm, 0.08mm, and 0.16mm.

|Labeled w (mm) (called a in |S (meters) |L (m) |s/L (~sinθ) |Calculated w (nm) |
|the device) | | | | |
|0.02 |0.03 |1 |0.03 |21093.333 |
|0.04 |0.015 |1 |0.015 |42196.667 |
|0.08 |0.0075 |1 |0.0075 |84373.333 |
|0.16 |0.004 |1 |0.004 |158200 |

Table 1: Results for slit width.

Using units of nanometers (10-9 meters), the widths are 2.0 x 104 nm, 4.0 x 104 nm, 8.0 x 104 nm, and 16.0 x 104 nm. The wavelength of the laser light is known very precisely; it is 632.8 nm.

1. The single slits device is placed in between the laser beam and the screen. In order to mark the positions, take the following page of the Course Pack and fold it so that one of the rectangles can be taped to the screen. The positions of the interference maximum (the big bright spot) and minima (the first dark spots on either side) can be marked with a pencil. This page should be used for both exercises today, using different rectangles for Part (A) and Part (B). When finished carefully remove the tape and turn it in along with the rest of your write-up.

Aim the laser through each of the four slits in turn, each time marking the positions of the minima and maxima.

2. Measure the distance 2s between the two minima on either side of the center (brightest) maximum of the intensity pattern. Divide by 2 and record the value for s in Table 1.

3. Calculate s/L ( ( sin θ ) for each slit and enter this in Table 1.

4. Use Equation (3) to find the actual slit width for each of the four slits. Enter the results in the last column of Table 1.

5. Looking at all your measurements you should be able to see a clear relationship between the slit width and the distance to the first minimum s. The most arrow slit for which you measured s was 0.02 mm. Suppose you replaced the 0.02 mm slit with one of width 0.01 mm; would s increase or decrease? Approximately, what would you have measured for s for such a slit?
If we replaced the 0.02mm slit with one of 0.01mm, S will increase, the S would be measured as 0.06mm.

[pic]

PAPER FOR SCREEN

Part B: Babinet’s Principle

Discussion

As we learned saw in exercise (A), the passage of light through a narrow slit results in a diffraction pattern. This is a general property of waves. In the context of Quantum Mechanics, it can also be understood as the result of the Uncertainty Principle on the passage of photons of light through the narrow slit.

If a wire of diameter d equal to the width of a narrow slit w, is placed in the path of a laser beam, what can we expect to observe on a distant screen?

For the following exercise, remember that the wavelength of the helium-neon laser light is λ = 632.8 nm.

[pic]

Figure 3: Geometry for the measurement (top view).

Part B: Setup and Data Taking Procedure / Questions

1. Choose the line in the line/slits device. Re-tape the paper on the screen so that a blank rectangle is showing. Aim the laser at the wire, so that you can observe the intensity pattern on the screen.

2. Mark the position of the direct laser beam, as well as the position of the first diffraction minimum on each side of the beam. If your laser is well aligned, these will show up at equal distances from the direct beam.

3. The distance s in the wire experiment in meters is _____0.008 meter_____________________.

4. The same equation for the position of the first diffraction minimum applies to the wire as to the narrow slit, with the diameter of the wire d replacing the width of the slit w. Hence we can write Equation (3) as

d = λ L /s . (4)

The distance L in your experiment in meters is _____1 meter______________________.

5. Use Eq. (4) to find the diameter d in nanometers.
632.8x1/0.008=79100nm

The similarity in the results for light diffracted from complementary objects (e.g. a slit versus a wire, or a disk versus a hole) is called Babinet's principle.
Part C: Two-Slit Interference

Discussion

The relation between the wavelength λ of the light, the slit spacing d and the angle between the central maximum on the beam axis and the next maximum where the intensity of light reaches a peak is:

λ = d x sin θ (5)

The geometry is shown in Fig. 4. L is the distance between the slit opening and the screen, and s is the distance between the central maximum and the first principle maximum. These bright spots are also known as “fringes”. Unlike the pattern for single-slit interference, the fringes are nearly equally spaced, if the screen is sufficiently far away. Hence the distance s can be obtained more accurately by measuring across several adjacent maxima and then dividing by the number of s intervals. For example, you can measure the distance spanned by five fringes and then divide by four to find s. Even better data would be obtained by measuring the distance spanned by eight fringes and then dividing by seven.

In terms of s and L, when the angle is small sin θ ( s/L, and we have

λ = ds /L . (6)

[pic]

Figure 4: Geometry for the measurement (top view).

Part C: Setup and Data Taking Procedure / Questions

SAFETY NOTE: Do not stare directly into the laser beam. If laser light happens to flash into your eye, just move your head away.

1. There are four pairs of slits in the double slit device. We wil use only 2. Read the spacing between the slits off of the slide frame and enter the values in Table 1. Note that the slit width is much smaller than the distance between the slits. The small slit width will give rise to a single-slit diffraction pattern on the screen (as we saw in part A today) which is large compared to the narrowly spaced two-slit interference pattern. Both effects are seen in this experiment.

3. Record the distance L from the slit device to the screen in Table 1. Fold the same paper you used in part A so that one of the rectangles can be taped to the screen.

|Distance d (mm) |S (meters) |L (m) |s/L (~sinθ) |λ =ds/L (nm) |
|a=0.04mm | | | | |
|0.25 |0.0025 |1 |0.0025 |625 |
|0.50 |0.00128 |1 |0.00128 |640 |

Table 2: Results for wavelength.

4. Aim the laser through the first pair of slits, and mark the positions of the finges (maxima) on the paper. Record in Table 2 the distance s by measuring the distance between several finges and then dividing by the appropriate number.

5. Calculate and record in Table 2 the results for s/L. Then using the labeled value for d, calculate λ using Equation (6), and enter the results into the table. Show the calculation below. The result for λ should be the wavelength of the light for the helium-neon laser.