2. Building a Laser Ruler. Measuring distances to high precision is a critical g
ID: 1400250 • Letter: 2
Question
2. Building a Laser Ruler. Measuring distances to high precision is a critical goal in engineering. Numerous devices 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 1052 nm to a 1075 nm beam, you notice that you must move the laser 5.155 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? (You may assume the small- angle approximation applies.)Explanation / Answer
We know that the path difference = Yd/D where Y is the distance from the central maxima on the scree , d is the seperation between the slits., D is the distance of screen from the source.
And for maxima this path difference is = nP where P is wavelength.
Therefore Yd/D = nP
Y = nPD/d
when the wavelength was 1052 nm say the screen was at distance of D m
when the wavelength changed to 1075 nm then the distance of the screen will be (D - 0.05155) m
And as it is given that the locations of maxima and minima is same for both cases
then we will write Y for first case
Y1 = nP1D/d
And for second case Y2 = nP2(D-0.05155)/d
On equating Y1 and Y2
P1D = P2(D - 0.05155)
D = 2.409 m
so earlier the screen was 2.409 m away
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