Then answer these:

A. Describe how you made the measurements using the images on the screen and the scale below them. Estimate the errors in the fringe spacing for each case, and then pair up the separation of the slit and its mirror image d with the spacing of the dark fringes ?x and report them here.

The wavelength of the light responsible for the patterns would be

lambda equals space left parenthesis capital delta x right parenthesis cross times left parenthesis d divided by ell right parenthesis

? = (?x d / ?)

as describe on the class website.

B. For each one, find a wavelength, then average them to give a mean value with a standard deviation for the set of data. Convert this average and its uncertainty to the commonly uses units of angstroms, microns, and meters.

C. In the image for the dial reading 45, the white fringes are big and show obvious color. What is the ordering of the colors and why does that occur?

Fundamentals of Physics || Laboratory (224) Dashboard / My courses / P_hysics II Lab 224 l 18 October 24 October / Measure Lloyd's mirror interference , a double sli... Measure Lloyd's mirror interference a double slit with only one slit Interference with a reflection To achieve interference of light we have to combine two or more beams that remain in step - we say "in phase" -- for all time. For most light sources this means we must take the same incoming light and provide two different paths for it. As you would see in the physics explanation on this website, one method is to use two slits or pinholes that sample light from a distant source at two places. The light that passes through them will be in phase because the paths from the distant source to the two apertures are the same, In the wave picture the disturbances of the electromagnetic field coming out of them will be in step, In the photon picture of light, each photon has equal probability of going through either aperture. At some distant point where light from either aperture may overlap the amplitudes of the waves add and interference results. Lloyd's mirror was used as early as 1834 to create this situation and demonstrate the wave nature of light, as well as to enable a measurement of its wavelength. Credit: Wikipedia Stigmatella aurantiaca CC by SIX3.0 In this illustration a small region of light (usually a narrow slit parallel to the mirror's surface) illuminates a flat mirror and nearly grazing incidence and also a screen that is perpendicular to the mirror at its far edge. Light may directly reach the screen (shown here in blue) or may reflect off the mirror (shown in red) to interfere at each point on the screen. It is geometrically equivalent to two slits separated by twice the height of the first above the mirror's surface. Do not confuse the colors shown here with the different colors of light! They are used so you can tell one path from another, but the two paths are possible for any color or wavelength. Dial reading 55 Scale in millimeters All of these images are with the camera in a fixed position. We are only moving the slit to effect a change the separation of the two slits of the double slit interferometer. 5. Observe and comment on the patterns you see in the interference fringes as the spacing is changed. 6. Using our calibration of D0 validated by the direct measurement with a scale in # 4, what is the slit separation 11 in each case for dial readings ,, 43, 45, 47, 49, Si, 53, and 55 that produced the fringe patterns in these images? Note that the uncertainty in the dial reading is :1, What uncertainty will this introduce into a measurement of wavelength that depends on d? The first dark fringe is at the mirrors edge, then there is a bright fringe, then another dark one, and so . You should determine the separation between two dark fringes in millimeters for each of the 7 images shown. The image scale shown is a photograph of the precision millimeter ruler at the position of the back of the mirror. While there is software we could use to precisely fit the fringe patterns, since we are only trying to find an approximate wavelength for light with this method you can do it more simply by making a direct measurement on your display. This will be most accurate for the small slit separations that produce the big fringe spacings, but the error in the slit position is also larger in those cases. You can use another scale and measure the images of the patterns and of the millimeter scale, or take a plain paper and place it at the displayed image. Mark the paper and then move it down to the scale and measure the separation of the marks. If you measure the spacing across several fringes and divide by the number of fringes in that measurement, it will be more accurate. Try to find a spacing for each image of the distance from the center of one dark fringe to another. 7. Take notes on what you did to find the spacings, and then record the fringe spacing x for each case. Pair up the separation of the slit and its mirror image 0? with the spacing of the fringes AX for that case. We will ask for the data, and for a description of how you made the measurement. The distance from the slit to near side of the mirror where the fringes were observed was 80 mm. According to the analysis of double slit interference that we showed in this lab preparation, the separation of two adjacent bright (or dark) fringes is such that Ax : Af/d where xi is the wavelength, 3\" is the distance from the slits to the screen, and d is the separation of the slits, 2k in this case. 8. What is the approximate wavelength of white light for the cases you measured in #7 above. Find an average. Convert the units of the average of your measurement to these commonly used scales: - Angstroms A or 10'8 cm I Microns yarn or 103 mm or 106 m - Meters 9. In the image for dial reading 45 the white fringes are big and show obvious color, What is the ordering of the colors and why does that occur? 10. Based on that image, what is the ratio of the wavelength or red light to the wavelength of blue light? Note that that ratio is independent of the uncertainty in d for this small slit distance. Last modified: Friday, 22 October 2021,9125 AM 4 Watch one single photon interfere with itself Jump to... : Use a CCD camera > }--- >4 The source in this figure is h above the plane of the mirror's surface. It is I? from a vertical plane on which the light will be detected, something usually called a "screen" but it can be in freely open space. Two paths are shown, the direct one to the screen, and a reflected path taking a longer distance and more time to reach the screen. The reflected path appears to come from another "virtual" slit that is below and behind the mirror as seen from the screen, You could imaging removing the mirror and having another source at that virtual point and have the same geometry for the light. This is simply the geometry for the two-slit or double slit interferometer. 1. Explain why the separation of the two slits is 2h, The reflected light is different from the direct path light because of its interaction with the surface. A wave meeting a surface and then developed again leaving it changes its phase by one half a cycle on reflection, Since phase is measured as an angle from O to 360 degrees or from 0 to 2:: radians, we describe this by saying that the phase changes 180 degrees or If radians upon reflection. Apart from that effect, this experiment is exactly equivalent to Young's double slit. 2. If the two beams have paths that differ by exactly one wavelength A in Young's double slit, do they add constructively to make a bright interference region, or destructively to make a dark one? 3. Asking the same question again, but for Lloyd's mirror, is the interference in this case constructive or destructive? Here is our version of this experiment. \"\"t Dial ga'L'ige '- \"'T'h -1, 1 V The lights source in this photo is an LED flashlight with the reflector removed. It is a "point" source that illuminates an adjustable slit, A knob on the far side allows us to change the slit opening. The slit is on a slide that has a screw which positions it left or right with respect to the plane of the mirror's surface, It has been carefully rotated about a horizontal axis to make the line of the slit opening parallel to the plane of the mirror. Every point on the slit is equivalent to every other point when this is done. On our side of the slit, the light that leaves it illuminates a precision flat mirror, There is an aluminum coating on this side of the mirror, it's front surface, from which the light may reflect. From this side looking toward the illuminated slit we see the slit and its mirror image W the two slits of the double slit experiment. \fIn the lower view we have added a millimeter scale so that you can see the separation of the slits, While in this image the two slits both appear "real", the one on the right is the direct image and the one on the left is off the mirror. The separation of the real and virtual slits is twice the distance of the slit on the right above the mirrors surface. ___n The dial gauge is a precision tool that uses a a system of gears to alter the reading on a dial when a plunger is depressed. The smallest reading on this scale is 0.001 inches. Since 1 inch is 25.4 mm, the least count of the dial gauge is 0.00254 mm. We frequently use the unit of the micromillimeter or "micron" pm, which is 10 meter or 103 mm. In that unit, one division of the dial scale is 2.54 microns. When the image shown above was taken the dial read 75 thousands of an inch. We may change that separation using the screw adjustment seen in these photos. The fringes disappeared when the dial read 42 thousands, Use the millimeter scale in the photo to make a measurement of the separation of the two slits at this setting, 4. What as the apparent separation of the slits when the dial gauge read 75 based on the millimeter scale in the image above. Estimate the separation to 0.1 mm. Compare that to the dial gauge, which will give the distance of the slit above the mirror plane. Since the light disappears when the gauge reads 42 that means the slit is behind the mirror at that setting. Therefore, d = 2 x (D D\") x 0.0254 where D is the dial gauge reading, D\" = 42 is the zero point of the scale, and d is the separation of the real and virtual slits in millimeters. The factor 0.0254 is the conversion to millimeters from thousands of an inch. How does this compare with the separation we see in the image above? The dial gauge will be more accurate than a millimeter scale when the separations are small. Interference is observed anywhere beyond the mirror in the space where the camera that took these pictures was located. To effectively have a full mirror in front of the image sensor we would have to place the sensor exactly at the back of the mirror. We achieve the optical equivalent by focusing on the near edge of the mirror, In this plane the light from the real and virtual slit has diverged because of diffraction at the slit itself fills the space with overlapping light. Closer inspection reveals interference fringes. They become more distinct when we move the slit closer to the plane of the mirror, effectively reducing the separation of the slit and its mirror reflection. We start with a small separation just large enough to let light through and create a pattern we can record. These images show a close up view of the light spot where interference occurs in Lloyd's mirror.