Chapter 10 DIFFRACTION GRADING SAFETY NOTES

Transcription

1 Chapter 10 DIFFRACTION GRADING SAFETY NOTES Do not look directly into the laser cavity, or at any reflections of the laser caused by shiny surfaces. Keep beam at bench level so as not to accidentally shine the beam into the eyes of another person 3.1 Purpose To determine the wavelength of diffracted light by means of a transmission grating and slit separation distance of this diffraction grating. 3.2 Introduction A diffraction grating is a device based on Young's double slit principle and, in the same way, it produces interference through diffraction. Figure 1. Here d=a+b Figure 1. Diffracting slit pattern. In Young's double slit experiment, passing light through narrow slits in an opaque screen generates an interference pattern. A diffraction grating, however, has hundreds or even thousands of slits. By increasing the number of effective point sources contributing to the interference pattern, the maxima become very sharp, thus increasing the ability to resolve closely spaced wavelengths. Figure 1 - The Diffraction Grating. I-incident beam, II- diffraction grating and III-diffracting beams. Although a diffraction grating is often pictured as parallel slits in an otherwise opaque screen, gratings are usually constructed of a transparent material with closely spaced "grooves." (Figure 1) Early gratings were created by scribing closely spaced lines in the surface of a glass plate with a diamond stylus, but modern gratings are often made by holographic techniques. Both

2 transmission and reflection gratings may be found in instruments used to study the spectra of light sources. In this lab, you will use a transmission grating. The equation that defines the positions of the maxima for a diffraction grating is the same as that for Young's double slit: d sin φ = λm = 0, 1, 2, 3,... (1) where d is the separation between two adjacent slits, φ is the angle through which the m-th order is diffracted, and λ is the wavelength of the light. Note that d is not usually given; more likely, you will be given the number of grooves per unit length (called lines/cm or lines/mm, for example.) Unlike the double slit, the diffraction grating produces interference fringes at wide angles, so the small angle approximation may not be used to simplify Equation 1. We denote distance from grating to the screen L, distance from central maximum to mth maximum lm Figure 3. Using equation 2 we can find d or λ. (2) Figure 3. Geometric construction of many -slit experiment Pre lab questions: PQ1: Why we can use approximation at small angles? 3.3 Procedure 1. Set up the laser and grating so that the laser beam is normally incident on the grating. Observe the pattern produced on a screen about one meter from the grating. 2. Measure and record the distance from the grating to the screen. 3. Measure and record the distances to the first, second and third diffraction maxima on both sides of the central maximum.

3 3.3.1 Apparatus The following pieces of equipment are required for this experiment: Laser: Ne unknown wavelength laser diffraction grating with different d slit size Apparatus IN-LAB TASKS IT1: For each maximum on either side of the center maximum, calculate the diffraction angle λ using the inverse tangent function IT2: Using the known value of line spacing for your grating, calculate the wavelength of the unknown laser for each maximum measured. Calculate the average wavelength. Compare to the known value by computing percent error. IT3: For each maximum on either side of the center maximum, calculate grating of unknown diffraction gratings. Calculate the average wavelength. Compare to the known value by computing percent error. Discussion/Conclusions: Did your results agree with the results of the diffraction grating equation? Why or why not? What would you have observed if you used a shorter wavelength light source? What would you have observed if you used a grating with closer line spacing?... Bonus The grooves on a CD act like a reflection grating. Measure the line spacing of a CD by reflecting laser light from the grooved surface. (Hint: if the laser strikes the CD at right angles, Equation 1 may be used. Otherwise, you need to use a form of the grating equation for light striking at a non-zero angle of incidence.) The area of the CD's pits is approximately d2/2, where d is the groove spacing. How many pits can fit in the usable area of a CD? At 8 bits per byte, approximately how many megabytes can the CD hold? Compare your calculation to the stated CD capacity.

4 Template I Diffraction Grating.Data/Results Grating lines/mm Grating line spacing (d) Distance to screen (x) order (m) Distance to m-th max. (ym) m wavelength (measured) φ m measured wavelength average measured wavelength known wavelength Uncertainty calculation

5 Chapter 11 PROPAGATION OF LIGHT. NUMERICAL APERTURE IN OPTICAL FIBRES SAFETY NOTES Do not look directly into the laser aperture, or at any reflections of the laser caused by shiny surfaces. Keep beam at bench level so as not to shine the beam accidentally into the eyes of another person. Align the focused beam from the microscope objective to the fiber end with the room lights on. 2.1 Purpose The purpose of this experiment is to study propagation of light in optical fibres, numerical aperture (NA) of a plastic multimode fiber by different methods. measure 2.2 Introduction Fibre optic cables are used in transmitting data in communication systems for making physical links among fixed points. Since it carries signal as light, optical fibres cannot pick up electromagnetic interference. The center of fibre is the core, which has a higher refractive index compare to the outer coating and this difference makes light to propagate through central core because of total internal reflection and is the means by which an optical signal is confined to the core of a fibre. In order a light to be guided through it must enter the core with an angle that is less than so called acceptance angle for the fibre. A ray entering the fibre with an angle greater than the acceptance angle will be lost in the cladding. The acceptance angle also called numerical aperture. So, the numerical aperture (NA) is a measurement of the ability of an optical fibre to capture light. 2.4 Theory Propagation of light through the core of an optical fibre depends on materials of core, cladding and their refractive index difference. Snell s law explains the propagation of light along an optical fibre. This law explains relationship between angles of incident and transmission on the interface between two dielectric mediums: n1 sin n2 sin (1) If the angle of incident is increased, there will be a point when angle of refraction will be equal to 90 0 which is referred to as critical angle. Therefore, Snell s law transforms to the relationship of critical angle, refractive index id core and cladding: sin n 2 (2) n 1

6 If the angle of incident is increased slightly beyond the critical angle, refractive angle will also be increased beyond 90 0 level and 99.8% of incident light reflects towards n1 medium. So, light can propagate through a dielectric medium of refractive index n1 surrounded by a cladding dialectic material with n2 where n1>n2 in zigzag mode and for incident angle. The speed of light traveling through a optical fibre with refractive index n=1.5 is calculated from n=c/v, where v is speed of light in the fibre and c-speed of light vacuum. The acceptance angle can be calculated from refractive indices of the core and cladding using formula arcsin n n The numerical aperture of the fibre is equal to the sine of the fibre acceptance angle and it is given by: n 1 n1 2 2 NA (3) Pre-lab questions 1. Sketch numerical aperture for a step index fibre and graded index fibre. 2.5 Procedure

7 2.5.1 Apparatus Optical fibre Neon Laser Experimentation Method The experiment is carried in semi darkness. NA will be calculated by investigating the light leaving the fibre. Equipment setup 1. Mount the laser using platform assembly on the optical table 2. Check that the laser beam is level and straight.mount the microscope objective assembly on the optical table approximately 2cm from the laser. 3. Place one end of the fiber into the slide holder and clamp gently. Adjust the position of the slide holder assembly so that the microscope objective focuses the beam on the end of the fiber. 4. Tape a sheet of 8 1/2 x 11 paper onto the optical table. 5. Turn the laser on and be sure the beam is focused on the end of the fiber near the microscope objective. Trace the light pattern onto the paper using a pencil and ruler. 6. Turn off the laser. 7. Measure full acceptance angle of the fiber. Measurement In-lab Tasks IT1: Determine the circle diameter R of the light and the distance L from the fibre to the screen. Calculate the acceptance angle and by taking the sine of the acceptance angle find the numeric aperture of the fibre. IT2: Repeat the measurement and tabulate your results. Plot NA as a function of the distance L and attach the plot. Calculate experiment uncertainties.

8 Discussion/Conclussion PT2: Comment on the different factors influencing any inaccuracies you may find. PT3: Compare and comment on your result by comparison with manufacturer value for the cable (SH4001 Super ESKA Polyethylene Jacketed Optical Fiber Cord)

9 Chapter 12 GLASS SLIDE REFRACTIVE INDEX DETERMINATION BY MICROSCOPE 12. Purpose The purpose of this exercise is to study working principles of Microscopes and telescopes and determine refractive index of a glass slide Introduction This exercise is intended to introduce basic concepts of measurement using microscopes Theory Light can be reflected or refracted at the interface/boundary surface depending on the angle of incidence. When light enters from one medium to another medium it will be refracted according to Snell's law. For example if light is traveling from air to water, then the refracted beam is bent towards the normal. Light going out off a point C and incident to a medium with smaller optical density experience a bending toward normal plane. The light appears higher than it actually is at distance a, Figure 1. This phenomenon allows us to calculate a refraction index of a glass. Figure 1. This light from point C travels in the air after it has crossed over the boundary of two medium - glass slide and air making angle ψ with the normal line drawn perpendicularly dawn to the surface. The amount of bending which a light ray experiences can be expressed in terms the difference between the angle of refraction and the angle of incidence and according to according of law of sines, sin angles of incidence and angle of refraction can be expressed by the following formula: sin n sin (1)

10 This light beam looks like coming out from the point C. From the drawing, the height of C is a =AC-Ac. From the ABC and ABc triangles: AB AC tan and AB Ac tan (2) Taking into an account AC=d and Ac=a', we can write: d a 1 d d a tan tan (3) Since the angles are small, tangents of angles can be replaces by sines: d a 1 d d a sin sin (4) From this formula, if we know the thickness of the glass slide and the height of point C, then we can determine the refraction index of a glass slide. The thickness of the glass slide can be measured with a micrometer. The C point s height can be measured with a microscope. Pre lab questions: 1. Sketch optical scheme of a microscope and a telescope. Why tan ψ can be replaced by sin ψ for small angles? Procedure Apparatus Microscope Micropmeter A glass slide Experimentation METHOD There are two parts based to two methods of measuring the height of point C. Equipment setup

11 Part I. Turn on the sodium lamp and allow it to warm up. The lamp is ready to use when the light is yellow-orange instead of pink. Position the lamp in front of the microscope's mirror. Use a diffuser or layers of Kimwipe to reduce the brightness of the light. Put a marker on the slide and place the slide on the stage of the microscope. Search for the marker through the microscope and when you find it, position at the center of the viewing field and bring it into clear focus. Write down the tuning position measured by the Vanier ruler of the microscope. Place another glass slide on top of the first one with the marker and bring it into the focus. Write down the tuning position again. Difference in both tuning positions equals to the height of point C. Part II. d n (1) d a In this method a marker is placed on both side of a glass slide. A visible thickness is equal to difference of tuning positions of both markers. Place a glass slide on the stage of the microscope and bring a marker into the focus. Write down the tuning position measured by the Vanier ruler of the microscope. Bring another marker which is at the bottom into the focus. Difference in both tuning positions equals to the a. Refractive index can be found from: MEASUREMENT In-lab Tasks d d n a 1 (2) d a IT1: Calculate the refraction index n for both methods.. IT2: Repeat the measurement and tabulate your results. Calculate experiment uncertainties. Discussion/Conclusion PT2: Comment on the different factors influencing any inaccuracies you may find. Which method is more accurate? PT3: Compare your result with expected value for the glass.

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13 Chapter 13 Wavelengths of mercury lamp specter 13.1 Purpose To determine the wavelengths of Hg lamp specters and angular dispersion of a grating by means of a transmission grating Introduction The diffraction grating, a useful device for analyzing light sources, consists of a large number of equally spaced parallel slits. A section of a diffraction grating is illustrated in Figure 1. A plane wave is incident, normal to the plane of the grating. The pattern observed on the screen is the result of the combined effects of interference and diffraction. Each slit produces diffraction, and the diffracted beams interfere with one another to produce the final pattern. The waves from all slits are in phase as they leave the slits. However, for some arbitrary direction measured from the horizontal, the waves must travel different path lengths before reaching let us say max intensity point. From Figure 1, note that the path difference between rays from any two adjacent slits is equal to d sinφ. If this path difference equals one wavelength or some integral multiple of a wavelength, then waves from all slits are in phase and a bright fringe is observed on the screen. From ABC: BC=AB sin = d sin (1) Therefore, d sinφ=kλ, (2) this is for maxima condition in the interference pattern when K= 0, 1, 2, 3,...K is diffraction order.

14 Figure 1. Geometric construction of multi slit interference We can use this expression to calculate the wavelength if we know the grating spacing and the angle. If the incident radiation contains several wavelengths, the mth-order maximum for each wavelength occurs at a specific angle. All wavelengths are seen at φ= 0, corresponding to the zeroth-order maximum. The first-order maximum is observed at an angle that satisfies the relationship sinφ=λ/d; the second-order maximum is observed at a larger angle φ, and so on. The diffraction grating is most useful for measuring wavelengths accurately. Like the prism, the diffraction grating can be used to disperse a spectrum into its wavelength components. Of the two devices, the grating is the more precise if one wants to distinguish two closely spaced wavelengths. For two nearly equal wavelengths λ1 and λ2 between which a diffraction grating can just barely distinguish, the resolving power R of the grating is defined as (3) where λ=(λ1+λ2)/2. Thus, a grating that has a high resolving power can distinguish small differences in wavelength. If N lines of the grating are illuminated, it can be shown that the resolving power in the mth-order diffraction is R=Nm.Thus, resolving power increases with increasing order number and with increasing number of illuminated slits, where N is the total number of slits illuminated and m is the order of the diffraction 13.3 Procedure Experimentation Apparatus Hg lamp spectrometer diffraction grating

15 A schematic drawing of a simple apparatus used to measure angles in a diffraction pattern is shown in Figure 2. This apparatus is a diffraction grating spectrometer. The light to be analyzed passes through a slit (2), and a collimated beam of light is incident on the grating (4). The diffracted light leaves the grating at angles that satisfy Equation 1, and a telescope (6) is used to view the image of the slit. The wavelength can be determined by measuring the precise angles at which the images of the slit appear for the various orders. Figure 2. Diffraction grating spectrometer Part I. To determine wavelength of mercury lamp specter. IN-LAB TASKS IT1: Changing the angle of the telescope to either side of the center maximum, calculate the diffraction angle φ for different specters: left right 2 IT2: In the same way as in IT1 find φ for different K. Every maximum corresponds to a specter. Using λ=d sin φ/k calculate λ for all lines of the specter and fill out Table I IT3: Calculate uncertainties.

16 TEMPLATE Table 1 K left right D av av Uncertainty Part II. Determine the resolving power of grating In this exercise also the mercury lamp will be utilized. IT1: Changing the angle of the telescope to either side of the center maximum, calculate the diffraction angle φ for different specters as in IT1 of previous part I for two closely wavelengths and put them in Table II. IT2: In Using λ= λ2- λ1 calculate R and calculate uncertainties Table II K left right 1 2 R Rav R Uncertainty =404.7 nm (Violet) 2. = nm (Green) 3. = nm (Yellow) Discussion/Conclusions: Did your results agree with the expected values of the diffraction grating and wavelengths? Why or why not? What would you have observed if you used a shorter wavelength light source? What would you have observed if you used a grating with closer line spacing?...

17 Bonus The grooves on a CD act like a reflection grating. Measure the line spacing of a CD by reflecting laser light from the grooved surface. (Hint: if the laser strikes the CD at right angles, Equation 1 may be used. Otherwise, you need to use a form of the grating equation for light striking at a non-zero angle of incidence.) The area of the CD's pits is approximately d2/2, where d is the groove spacing. How many pits can fit in the usable area of a CD? At 8 bits per byte, approximately how many megabytes can the CD hold? Compare your calculation to the stated CD capacity.

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