Chapter 37395Section 37.7The Michelson InterferometerP37.41When the mirror on one arm is displaced by ∆A,the path difference changes by 2∆A. A shiftresulting in the reversal between dark and bright fringes requires a path length change of one-halfwavelength. Therefore, 22∆A=mλ, where in this case, m=250 .∆A==×=−mµ4250 6 328 10439 67afej..mmP37.42Distance =×=−2 3 82 101 7004. m=−449 104497mnmThe light is blue .P37.43Counting light going both directions, the number of wavelengths originally in the cylinder ismL12=. It changes to mLnnL222λλas the cylinder is filled with gas. If Nis the number of brightfringes passing, Nm mLn=−=−2121af, or the index of refraction of the gas isnNL=+12Additional Problems*P37.44(a)Where fringes of the two colors coincide we have dmmsinθλ′′, requiring ′=′mm.(b)=430 nm, ′ =510 nm∴′mm4304351nm510 nm, which cannot be reduced any further. Then m=51,
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