Measuring distances to high precision is a critical goal in engineering. Numerou

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.

sapling learming Map 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. object aser 1 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 1319 nm beam move the laser 1.155 cm closer to the object to align the same order maxima and minima with their original locations on the object. , you notice that you must How far was the laser originally from the object in meters?* (Assume the small-angle approximation applies.) Number 175 Im Previous & Give Up & View Solution Check Answer Next Exit

Explanation / Answer

formula

W=D*lamb(da)/d

using formula we make two equations for laser wave lengths

W=D*1064n/d.................1

W=(D-0.01155)*1075n /d...............2

divide the equations 1 and 2 we get

1=(D*1064n/d)/((D-0.01155)*1075n /d)

D*1064=(D-0.01155)*1075

11*D=12.41625

D=1.12875m=11.28cm

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