Measunng dtstances to high precision is a critical goal m engineering Numerous d

Question

Measunng dtstances to high precision is a critical goal m engineering Numerous devicos to exist to perform such measurements with many involving laser light Shining light through a double slit will provide such a niter if (1) the wavelength of the light beam and sJit separation is known and (2) the distanco the minima/maxima appoanng on the screen can bo measured But this m itself requires a physical measurement of distance on the object, Which may not be practical In an effort to create a "laser-beam ruter* that does not require ptaang a physical ruler on the object, you mount a Nd VAG 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 pnncipal wavelength of a Nd VAG laser, the laser is also switchaWe to numerous secondary wavelengths. mdud>>>>g 1052 nm. 1075 nm. 1113 nm. and 1319 nm

Explanation / Answer

Using Young's Double Slit Formula of y(bright) = Lm/d can solve this problem

For this problem, it must be realized that we are asked to find where y(bright) will be the same for two different wavelengths () and two differentscreen Distances (L). The order (m) and the slit distance (d) will remain the same.

The first wavelength of 1064 nm is a distance L away from the screen

The second wavelenght of 1113 nm is L - 3.155 cm away, or 3.155 cm closer

Since y(bright) for situation 1 must equal y(bright) for situation 2, you can set the equations equal to each other

1Lm/d = 2(L-3.115 X 10^-2)m/d. The values of m and d will be the same on both sides of the equation and can be cancelled out leaving

(1064 X 10^-9 L) = (1113 X 10^-9) (L - 3.115 X 10^-2)

Distribute on the right side of the equation

1064 X 10^-9 L = 1113 X 10^-9 L - 3.467 X 10-8

Solving for L provides...

3.467X 10-8 = 4.9 X 10-8 L

so L = 0.708 m

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