Measuring distances to high precision is a critical goal in engineering. Numerou
ID: 1408891 • Letter: M
Question
Measuring distances to high precision is a critical goal in engineering. Numerous devices to exist to perform such measurements, with many involving laser light. Shining light through a double slit will provide such a ruler if (1) the wavelength of the light beam and slit separation is known and (2) the distance the minima/maxima appearing on the screen can be measured. But this in itself requires a physical measurement of distance on the object, which may not be practical. In an effort to create a "laser-beam ruler" that does not require placing a physical ruler on the object, you mount a Nd:YAG laser inside a box so that the beam of the laser passes through two slits rigidly attached to the laser. Although 1064 nm is the principal wavelength of a Nd:YAG laser, the laser is also switchable to numerous secondary wavelengths, including 1052 nm, 1075 nm, 1113 nm, and 1319 nm. Turning on the laser, you shine the beam on an object located nearby and observe the interference pattern with a suitable infrared camera. By switching from a 1064 nm to a 1319 nm beam, you notice that you must move the laser 3.155 cm closer to the object to align the same order maxima and minima with their original locations on the object. How far was the laser originally from the object in meters?* (Assume the small-angle approximation applies.)Explanation / Answer
for a double slit interference pattern,
the distance of maxima from the central bright spot is given by
y=m*lambda*D/d
where m=order of the bright spot
lambda=wavelength
D=distance of the slit from the screen
d=slit width
keeping m and d constant,
to get same y for different wavelength, lets say lambda_1 and lambda_2,
m*lambda_1*D1/d=m*lambda_2*D2/d
where D1 is the original distance and D2 is the adujsted distance,
==>lambda_1*D1=lambda_2*D2
==>1064*D1=1319*D2
==>D1=1.2397*D2....(1)
given that D1-D2=3.155 cm=3.155*10^(-2) m
==>0.2397*D2=3.155*10^(-2)
==>D2=0.13164 m
then D1=1.2397*D2=0.1632 m
hence the original distance of the laser from the object is 0.1632 m