Physics Hour Examination Light and Optics - Version 1

Transcription

1 Physics Hour Examination Light and Optics - Version 1 How Do We See Colors? Warning: Multiple Choice questions may have more than one correct answer. They are graded 3 points of each correct answer circled and minus 1 point for each wrong answer circled. : Reci Section 8:30 11:00 12:00 Physical Constants: Electric charge of the electron = e = 1.6 x C Speed of light = c =3 x 10 8 m/s Mass of the electron = me = 9.1 x kg Planck's constant = h = 6.63 x Js = 4.14 x evs Electron volt of energy = 1eV = 1.6 x J Situation No. Maximum Pts Earned Total 100 Bonus 3 10 Bonus 3 20 Grand Total 130

2 Situation 1: Circle the letter in front of every correct answer. (3 points for each correct answer, -1 for each wrong answer, then scaled to 18 points max.) The eye can detect wavelengths that range from 400 nm to 700 nm, where 1 nm = 10-9 m. The color of this visible light ranges from violet at 400 nm to red at 700 nm. This range closely matches the wavelength range of maximum emission from the sun. The relationship between the wavelength of light and the energy of each quantum is E = hc/λ where h is Planck's constant, c is the speed of light in a vacuum, and λ is the wavelength. Another form of this equation is E = 1240/λ where λ is in nm and E is in ev (electron volts). Light can be emitted when atoms make transitions from excited states to lower-energy states. Each quantum of emitted light carries energy equal to the difference between the energies of the states involved. For the emitted light to be visible, it is necessary that the states involved be separated by the proper energies. Visible light arises from atomic transitions between energy levels separated by approximately 1.78 to 3.10 ev. For example, assume that the energy levels of a hypothetical atom are the following: Energy Level ev Energy Level ev Energy Level ev Energy Level ev Energy Level ev Energy will be emitted when an atom makes a transition from a higher to a lower energy level, but visible light will result only when those energies fall within the prescribed range. Light is also emitted from a hot object by a process called blackbody radiation. The most intense wavelength, λ max, of blackbody radiation is given by Wien's displacement law, λ max = 2.9 x 10 6 / T, where T is in kelvins and λ max is in nm. 1. The most intense wavelength emitted by the sun is 480 nm. What is the approximate temperature of a blackbody that emits its most intense radiation at the same wavelength? A. 4,100 K B. 6,000 K C. 7,200 K D. 9,000 K 2. What is the maximum number of emission lines of visible light that could be observed in the spectrum of the hypothetical atom described in the passage? A. 1 B. 2 C. 5 D A blackbody appears white when its temperature is approximately 6,000 K. Which of the following statements explains the color of light emitted at this temperature? A. The object is not hot enough to emit red light. B. The object is too hot to emit blue light. C. White light is the most common wavelength being emitted. D. The object is emitting some light from all colors of the visible spectrum. 4. What is the wavelength of the light emitted when the hypothetical atom described in the passage makes a transition from Energy Level 4 to Energy Level 3? A. 477 nm B. 525 nm C. 600 nm D. 658 nm 5. As the power input to a light bulb decreases, the brightness decreases. How does the color of the emitted light change? A. The emitted spectrum shifts to longer wavelengths. B. The emitted spectrum shifts to shorter wavelengths. C. The most intensive light shifts to lower energy. D. The spectrum does not change. Page 2 of 5

3 Situation 2: Circle the letter in front of every correct answer. (3 points for each correct answer, -1 for each wrong answer, then scaled to 27 points max.) Flexible endoscopes are used extensively in medicine to visualize 6.For the best image quality, the internal structures such as the respiratory tract, stomach, and colon. The following conditions should be met. advantage of a flexible endoscope over a rigid endoscope is that it can A. The core of the fibers must not bend and thus go around corners. This means less discomfort for the absorb a significant amount of light. B. The cladding must have a higher patient and the endoscope can be advanced farther into the cavity of optical density than the core. interest. C. Light rays must be incident on the An endoscope has a number of channels, e.g. for irrigation, suctioning, core-cladding interface at angles of surgical manipulation, illumination, and imaging. Below is a incidence greater than the critical diagrammatic representation of the imaging components of a relatively angle. simple flexible endoscope. D. The endoscope must not be bent too acutely. 7.The critical angle of the corecladding interface is given by A. critical angle = sin -1 (n cladding /n core ) B. critical angle = sin -1 (n core /n cladding ) C. critical angle = sin -1 (1/n core ) D. critical angle = sin -1 (1/n cladding ) 8.If each fiber core is 1 mm in diameter, n core is 1.50, and n cladding is 1.20, what is the minimum length of light-absorbing material required at the ends of the fibers to prevent refraction of light into the cladding? A. 1 mm B mm C. 1.5 mm D. 2 mm 9. The effect of lens 1 is A. to possibly reduce overall chromatic aberration B. to produce a virtual, erect, and diminished image that is the object for lens 2 C. create a wider field of view D. to invert the image of the object Lens 1 focal length is -2 cm. Lens 2 focal length is 1 cm. Lens 3 can be easily removed and replaced with another lens. Also, the distance between lens 3 and the end of the optical fibers can be adjusted. Each optical fiber consists of a cylindrical core surrounded by a cladding. Light enters one end of a fiber and is total internally reflected repeatedly until it exits the fiber at the opposite end. 10.When light has travelled the length of the optical fibers it exits the ends of them and passes through lens 3, which acts like a magnifying glass. If an observer chooses a lens of 50 diopters, how far should lens 3 be from the end of the optical fibers to form an image at infinity? A. 2.0 cm B. 2.5 cm C. 3.0 cm D. 3.5 cm Page 3 of 5

4 Situation 3: (25 points) As a part of your job as an Olympic drug-testing expert, you have been asked to make a judgment on an Olympic athlete whose body fluid has been given an analysis using a standard spectrophotometer. A calibration curve of the appropriate body fluid was first taken, and then the body fluid of the athlete containing an unknown amount of a possible drug was taken. The data and the curves for both analyses are shown below. wavelength Calibration Unknown nm rel. intensity rel. intensity Spectrophotomete Calib Unknown Solu Wavelength (a) (15 points) You have found from the standard table of concentrations of drugs in this bodily fluid, that the forbidden drug, Neosynepherin, has a maximun absorption at about 575 nm and has an optical density as a function of concentation give by the equation OD(Neosynepherin) = 3.14 * (concentration of Neosynepherin in gm/liter of body fluid) Estimate the concentration of Neosynepherin in the body fluid of this athlete. Show your work. (b) (10 points) It is believed that 200 parts per million of Neosynepherin will enhance the performance of an athlete. Knowing that one liter of body fluid has a mass of 1000 gm, do you think the athlete should be ejected from the Olympic games? Explain your answer. Bonus points: (10 points) Select an appropriate graph and show the transmission of the body fluid containing the unknown drug as a function of wavelength. Label the axes. Show your work. Page 4 of 5

5 Situation 4: (30 points, 10 points for each correct answer and its explanation) As a part of your job as a health care provider, you have been asked to come up with a plan to help Americans pay for their health care costs. You have been presented with the following data: The cost of gall bladder surgery in the United States is given below: Year Cost 1950 $ $ $ $ $ $ 803* The Medicare Program went into effect in $ $ $ $ $ $ 4900 From these data, or an appropriate graph, estimate, and explain the process you use to make your estimate (a) when will gall bladder surgery cost twice as much as it did in 1980? Show your work. (b) the present annual percentage change in the cost of gall bladder surgery. Show your work. (c) the cost of gall bladder surgery near the end of your lifetime say, in the year Show your work. Bonus (20 points) Select an appropriate graph and show these data as linear function(s). Label the axes. Page 5 of 5