Some experiments require calibration of the equipment before the mea- surements can be made. Any random errors in the calibration will usually become Systematic errors in the experiment itself. To illustrate this effect, consider an exper- iment on the Zeeman effect, in which a magnetic field causes a tiny shift in the 4.27. frequency of light given out by an atom. This shift can be measured using a Fabry- Perot interferometer, which consists of two parallel reflecting surfaces a distance d apart (where d is typically a couple of millimeters). To use the interferometer, one must know the distance d; that is, one must calibrate the instrument by measuring d. A convenient way to make this measurement is to send light of an accurately known wavelength A through the interferometer, which produces a series of interfer- reference marks fringes wavelength is sent through a Fabry-Perot interferometer, it pro- Figure 4.3. When light of one duces a pattern of alternating light and dark fringes. If the air is pumped out of the interferome- ter, the whole pattern shifts sideways, and the number of complete fringes (light-dark-light) that pass the reference marks can be counted; for Problem 4.27. ence fringes like those depicted in Figure 4.3. If all the air is then pumped out of the chamber that houses the interferometer, the interference pattern slowly shifts sideways, and the number of fringes that move past the reference marks is 1)d/A, where n denotes the refractive index of air. Because n and A are known accurately, d can be found by counting N. Because N is not necessarily N =2(n an integer, the fractions of complete fringes that pass the reference marks must be estimated, and this estimation introduces the only serious source of uncertainty. (a) In one such experiment, a student measures N five times as follows: values of N = 3.0, 3.5, 3.2, 3.0, 3.2. What is her best estimate for N and its uncertainty? What is the resulting percent uncertainty in d? (b) The uncertainty you just found is purely random. Nevertheless, in all subsequent measurements using the interferometer, she will be using the same value of d she found in part (a), and any error in that value will cause a systematic error in her final answers. What percent value should she use for this systematic error in d?

Some experiments require calibration of the equipment before the mea- surements can be made. Any random errors in the calibration will usually become Systematic errors in the experiment itself. To illustrate this effect, consider an exper- iment on the Zeeman effect, in which a magnetic field causes a tiny shift in the 4.27. frequency of light given out by an atom. This shift can be measured using a Fabry- Perot interferometer, which consists of two parallel reflecting surfaces a distance d apart (where d is typically a couple of millimeters). To use the interferometer, one must know the distance d; that is, one must calibrate the instrument by measuring d. A convenient way to make this measurement is to send light of an accurately known wavelength A through the interferometer, which produces a series of interfer- reference marks fringes wavelength is sent through a Fabry-Perot interferometer, it pro- Figure 4.3. When light of one duces a pattern of alternating light and dark fringes. If the air is pumped out of the interferome- ter, the whole pattern shifts sideways, and the number of complete fringes (light-dark-light) that pass the reference marks can be counted; for Problem 4.27. ence fringes like those depicted in Figure 4.3. If all the air is then pumped out of the chamber that houses the interferometer, the interference pattern slowly shifts sideways, and the number of fringes that move past the reference marks is 1)d/A, where n denotes the refractive index of air. Because n and A are known accurately, d can be found by counting N. Because N is not necessarily N =2(n an integer, the fractions of complete fringes that pass the reference marks must be estimated, and this estimation introduces the only serious source of uncertainty. (a) In one such experiment, a student measures N five times as follows: values of N = 3.0, 3.5, 3.2, 3.0, 3.2. What is her best estimate for N and its uncertainty? What is the resulting percent uncertainty in d? (b) The uncertainty you just found is purely random. Nevertheless, in all subsequent measurements using the interferometer, she will be using the same value of d she found in part (a), and any error in that value will cause a systematic error in her final answers. What percent value should she use for this systematic error in d?

Inquiry into Physics

8th Edition

ISBN:9781337515863

Author:Ostdiek

Publisher:Ostdiek

Chapter8: Electromagnetism And Em Waves

Section: Chapter Questions

Problem 33Q

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