Suppose to test the actual resolution of a laser printer, you print out a set of

Question

Suppose to test the actual resolution of a laser printer, you print out a set of vertical lines with a constant spacing on a transparency film. You hold the film 5.00 meters from the wall and shine a red 650. nm laser through the film. A set of discrete dots results due to the diffraction of the light by the lines. The separation between the center dot and the next closest dot (i.e. n=1) is measured to be 15.4 cm. Using the Fraunhofer equation, n = d(x/L), (i) calculate the separation distance between the lines on the slide (in inches). Then from this, (ii) determine the resolution of the laser printer by calculating the number of lines per inch that can be printed by your printer (Hint: think about unit analysis).

Explanation / Answer

d = Distance between slits of the diffraction film =
x = distance between dots on the screen = 15.4 cm = 0.154 m
L = distance between screen and the diffraction film = 5.0 m

Now Plugging Values in -
n = d*(x/L)
1 * 650*10^-9 = d(0.154/5)
d = 2.11*10^-5 m

Now Converting from m to inches
d = 8.3 * 10^-4 inches

(ii)
If there is one line per 8.3*10^-4 inches.
Number of lines per inch =  1/(8.3*10^-4 ) will give us the
Number of lines per inch = 1205 lines per inch.

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