re all mankind minus one were of one opinion, and only ane the contrary opinion,

Question

re all mankind minus one were of one opinion, and only ane the contrary opinion, mankind would be no that one person, than he. silencing mankind re justified in silencing if he had the power, would be justified in We can never be sure that the opinion we are ing to stifle is a faise opinion and if we vere stifling SUPPL. PROBLEMS (1859) 1081 1083 ie would be an evii stil John Stuart Mill, Easay, On L 1081 In order to check the accuracy of a micrometer gauge block, which is supposed to be 1.3300 long, an engineer puts the gauge bloek into an interferometer and moves the interferometer airror through a distance equal to the length of the block. As he does so, he counts 4162 interference Interference pattern. (If he doesn't want to count them, he can use a photometer to record and count the intensity maxina.) The engineer is using standard red cadat um light (wavelength 6438 A ). the gauge block? Would the result be difterent if the measurement was carried fringes arossing a marker on the What is the actunl Length of 1082 A gas refrsctometer is constructed on the principle shown in the diagran Originally, both identical tubes, T1 and T2, are evacuated, and T, is kept evacuated while the gas to be tested is slowly adaitted to T2 to the pressure desired. As the gas 'ia adaitted, inter- ference fringes move across the cross-haire in the telescope. (The pattern is made up of eircular rings, as in the Kichelson interferometer, if a finite source is used.) (a) If the tubes are each L long, and if the interference pattern shifts by N dark fringes while the gas is being admitted, and the source emits wavelength in vacuum, what is the index of refraction of the gas, in terms f ,, L, and N? ("Fringe shift" neans a change fron dark to bright to dark (or brd+b). In a pattern of efreular fringes (as in the nodel interferometer in Physics 4) circular rings move in toward the center as one path (or as one index) changes and a given pofnt in the pattern changes froa dark to bright to dark as rings (b) what is n of the gas if the tubes are 30.0 em long, and the pattern shifts 10 fringes with wavelength 6000 R Two glass paraboloidal shells, having the equations shown, are placed in contact at the origin of the coordinate system. The material between the shells has index (less than n of the glass). Find the radius of the Nth bright interference viewed by reflected light, if the incident light has wavelength ° in air, in terms of N, k, m, n, and Prob.1077--

Explanation / Answer

1081. for a wavelength of lambda, when the interferometer mirror is moved by distance d in one arm

and number of fringes crossing the marker on the interference pattern is n

then

n*lambda = 2d

d = n*lambda/2

now givne

n = 4162

lambda = 6438*10^-7 mm

hence

d = 4162*6438*10^-7 mm / 2 = 1.3397478 mm

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