OPSE FINAL EXAM Fall CLOSED BOOK. Two pages (front/back of both pages) of equations are allowed.

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1 CLOSED BOOK. Two pages (front/back of both pages) of equations are allowed. YOU MUST SHOW YOUR WORK. ANSWERS THAT ARE NOT JUSTIFIED WILL BE GIVEN ZERO CREDIT. ALL NUMERICAL ANSERS MUST HAVE UNITS INDICATED. (Except dimensionless units like index of refraction). Problem 1: An underwater swimmer shines a beam of green light up towards the surface of the water. It strikes the water/air interface at an angle of 40 degrees. The refractive index of water is (a) At what angle does the refracted light emerge from the water? (b) If the green light has a wavelength of 514nm, what is the wavelength of the light in the water? (c) At what angle does the refracted light emerge from the water if the angle of incidence is 70 degrees instead of 40 degrees? EXPLAIN YOUR ANSWER. Problem 2: Following the procedures of Lab 7, a photodetector is tested to see if it responds linearly to the amount of light incident on its surface. The amount of light incident on the detector is controlled using neutral density filters. For the data shown in Figure 1, A. Below what power level is the photodetector linear? WHY? B. Using the data in the figure and table, determine the sensitivity (in units of V/W) of the detector in the linear power range. Voltage (mv) Power (mw) ND Power Voltage E E E E E E E E E E E E E E E E E E E E E E-03 Figure 1: Experimentally measured voltage from a photodetector as a function of incident laser power. Page 1 of 10

2 Problem 3: The figure below shows a type of interferometer called a Mach-Zehnder interferometer. Light from the laser is split into two equal parts using the first beam splitter. The two beams (Beam A and Beam B) recombine at the second beamsplitter and interfere with each other. Assume that the laser beam splits and then recombines at the exact centers of the cubic beam splitters. The dimension of cubic beam splitter is 1cm, and its index of refraction is 1.5, (a) What is the OPTICAL path length from where Beams A is split off and then recombined with Beam B? (For this part, you can assume correctly that the optical beam paths for Beam A and B are equal). (b) Imagine that you place a thin piece of plastic (refractive index 1.7) in the path of Beam A as illustrated in the picture. The thickness of the plastic is 0.01cm. What is the difference in path length between Beam B and Beam A with the plastic cube in its path? (c) Assuming that the laser is a He-Ne laser (wavelength of 632.8nm), what is the PHASE difference (in radians) between Beam B and Beam A with the thin plastic? Mirror Plastic Laser A 10cm B Mirror 5cm Problem 4: This question concerns Lab 5 and the measurement of the absorption coefficient for a colored liquid solution. Figure 2 illustrates the experiment looking from above. Note that the orientation of the sample box of liquid is exaggerated in order to help you think about the effect of moving the sample box during the measurement. Page 2 of 10

3 Mirror Sample Detector Laser Figure 2: Experimental setup for Question 4. Several questions in the lab report focused on why you should not move the box DURING the experiment. The essential point was that if the boxed moved, then the reference detector voltage would change resulting in a different calibration of Power with no dye present in the solution. Examine Figure 2 and discuss WHY moving the box changes the light detected by the photodetector. Specifically consider the following effects: (a) What effect does a changing angle of incidence of the light into the sample box have on the REFLECTED POWER from the box? HINT: you may wish to refer to the Fresnel equations on the equation sheet. How does this changing REFLECTED POWER affect the detected power? (b) What effect does the changing angle of incidence have on the path length through the liquid sample? Remember it is assumed that the path length through the sample is the inner width of the box. (c) What effect does the deviated beam (the solid line versus dashed beam path in Figure 2) have on the detected power? (d) What effect does NON-UNIFORMITY of the plastic box which contains the liquid sample have on the detected power? For example, let us assume that the plastic box is scratched in a spot. How and why does the detected power change if the light passes through the scratched spot relative to a pristine location? Page 3 of 10

4 Problem 5: An object is 30cm from a f = 10cm positive lens shown in the figure below, (a) On the diagram DRAW a ray diagram locating the image. (b) (c) (d) Calculate the location of the image relative to the lens. Is the image to the left or to the right or the lens? What is the magnification of the image? Problem 6: An object is 30cm from a f = 10cm positive lens as in the previous problem (you can use the results of Problem 5 here). In addition a positive f=20cm lens is added to the optical system as shown in the figure below. The distance between the two lenses is 11cm. f=10cm f=20cm (a) (b) (c) Calculate the location of the FINAL image relative to the f=20cm lens. Is the image to the left or to the right or the f=20cm lens? What is the TOTAL magnification of the image after passing through both lenses? Page 4 of 10

5 Problem 7: A green lamp emits light with a wavelength of 510nm. The lamp has a radiant flux of 6W and emits light equally in all directions. (a) What is the irradiance at a point which is a distance of 4m from the lamp? (b) A student uses a photodetector like the one in the OPSE lab to detect the green light. If the detector has an area of 5 mm by 5mm, what is the radiant flux (power) on the detector? (c) What is the luminous power on the detector in units of lumen? 4 Problem 8: The wavefunction of a wave is given by ψ( xt, ) = 30sin(150π x+ 10 t+ π) in SI units. (a) What is the amplitude of the wave? (b) What is the frequency of the wave? (c) What is the wavelength of the wave? (d) What is the speed of the wave? Problem 9: The speed V (phase velocity) of a wave is given by the equation Aλ 2πB V = + 2π λ where A and B are constants and λ is the wavelength of the wave. (a) Write this equation for the speed V in terms of the wavenumber k rather than the wavelength λ. (b) Show that the group velocity of the wave can be written as V g 2 1 A+ 3kB = 2 kbk 2 ( A+ ) Page 5 of 10

6 Problem 10: A large soap bubble (n=1.4) is viewed with light reflecting perpendicularly from the surface of the bubble. (The inside of the bubble is air.) In a section of the bubble, the film only reflects red light (620nm) strongly. What is the minimum thickness of the soap bubble? Problem 11: A laser (wavelength 850nm) emits a diffraction-limited beam with a 1mm diameter. How big a light spot would be produced a distance of 100m away? Problem 12: You are traveling in a plane at night and look down on a highway on which traffic is driving. The typical distance between headlamps on a car which is driving on the road is 2m. What is the maximum distance of the airplane to the car for which the two headlights are distinguishable as individual light sources? You can assume an eye pupil diameter of 4mm and a 550nm wavelength of light. Problem 13: Michelson Interferometer Lab Practical. On one of the setups in the lab, use the mirrors, beam splitter, and lens to generate localized fringes which are oriented PARALLEL to the floor. Problem 14: Consider the transmission filter C as well as the REFLECTION filters A and B given below. (a) If filters A, B, and C were stacked together as indicated in Figure 3a, what would be the spectrum of light (Give wavelength range in nm) which passes through the stack? (b) If order of the filters where switched as shown in Figure 3b, what would be the spectrum of light which would be finally reflected from filter B? Page 6 of 10

7 Reflected Power Filter A Reflected Power Filter B Wavelength (nm) Wavelength (nm) Power Transmission 1.2 Filter C Wavelength (nm) (a) (b)? A B C? C A B Figure 3: Use (a) for part (a) of Problem 14. Use (b) for part (b) of Problem 14. Problem 15: Light from an He-Ne laser (λ=632.8nm) impinges on two parallel slits in an opaque screen. An interference pattern forms on a distant wall from light that passes through the two slits. The separation between the slits is 0.3mm. You observe that the bright fringes on a screen 2m away. Kindly calculate the expected spacing between adjacent bright points in the fringe pattern. Problem 16: A 633nm harmonic (plane wave) EM-wave whose ELECTRIC FIELD is linearly polarized and a MAXIMUM in the y-direction at t=0 while the wave is traveling in the NEGATIVE z direction in vacuum. (a) What is the frequency (in hertz) of the wave? Page 7 of 10

8 (b) Determine ω and k for this wave. (c) If the irradiance (intensity) of the wave is 3mW/mm 2 what is the amplitude of the magnetic field? (d) What is the amplitude of the electric field? (e) In what direction does the MAGNETIC field point at t=0? Problem 17: As we discussed in class, people with normal eyesight have three different cells in their eyes. One type of cell is sensitive to red light, while another is sensitive to green light, and the last is sensitive to blue light. People who are color blind have either one of these three type of cells missing in their eye or the cells do not work properly. Let us assume that a particular person is color blind because they are missing the blue detector cells in their eyes. (a) If this color blind person were to look into the sky (NOT LOOKING INTO THE SUN, BUT LOOKING AT THE SKY) on a clear day, what color(s) would they see? JUSTIFY YOUR ANSWER. (b) Would this color blind person be able to see a traffic light? WHY? (c) What about a RED stop sign with WHITE lettering? WHY? Page 8 of 10

9 Problem 18: A beam of unpolarized, incoherent blue (450nm wavelength) light incident in air on a glass (n=1.5) interface at 45 degrees is partially reflected. (a) Calculate the reflectivity of the interface for light polarized PARALLEL to the plane of incidence. (b) Calculate the reflectivity of the interface for light polarized PERPENDICULAR to the plane of incidence. (c) Assuming that the total power of the unpolarized incident blue light is 10mW, how much total power (in mw) is reflected from the glass interface? Problem 19: (a) Using the following data (n o =1.800 and n e =1.755 at 514nm) for the very rare NJITium crystal, compute the MINIMUM thickness of NJITium required for a HALF waveplate. (b) Assume that incident light on the NJITium crystal is oriented as shown in the figure below. In what direction (choose from figures below) should the optical axis of the NJITium crystal be oriented so that the crystal acts as a ½ wave plate? EXPLAIN YOUR REASONING. Problem 20: A new type of protein which may indicate the presence of an alien species on earth, federcien, has just been discovered. You are using a setup similar to Lab 3 to determine its specific rotation at a wavelength of 632nm. You mix up a solution of 30g of federcien in 250mL of water. You observe that the polarization of 632nm transmitted through the solution rotates as shown in the figure. The path length of the sample is 5cm. (a) Is the solution predominately d-federcien or l-federcien? PLEASE EXPLAIN YOUR ANSWER. (b) Given that the specific rotation of federcien is 0.08 in units of (degrees-ml)/(cm-mg), what should be the measured angle of polarization rotation? Page 9 of 10

10 Problem 21: Lab Practical Lab 3 You are given an optic which is KNOWN to be a linear polarizer. Using this polarizer, determine which of the three unknown optics is also a polarizer. You can use the ambient room light as your source of light. (a) CIRCLE your answer: Optical component A B C is the polarizer. (b) EXPLAIN WHAT EXPERIMENT YOU DID AND THE RESULTS to support your conclusion. EXPLAIN YOUR REASONING. Problem 22: Consider the transmission of light (initially 1W of power, wavelength 500nm) through a slab of material of thickness L whose complex refractive index is given by n = nr + ini where n r =1.5 and n i =1.3. Assuming that ikonx iωt E(,) xt = Ee o (1) with n representing the COMPLEX refractive index, estimate the transmitted power through 25μm of this material. Page 10 of 10