A guy cuts a 3 micrometer wide slit in a piece of black construction paper and t

Question

A guy cuts a 3 micrometer wide slit in a piece of black construction paper and the shines a RED laser through it (Red light wavelength: 640*10^-9m). A screen is placed 4m behind the slit.

a)How wide is the central bright fringe on the screen?

b)He then cuts another slit parallel to the first one. If the distance between the two third order bright fringes is 5.5 cm apart, how far apart are the two slits?

c)He then cuts 237 more slits each separated by the same distance as the first two. At what angle relative to the central maximum do the third order bright fringes diffract now?

SHOW WORK AND CORRECT ANSWER TO GET POINTS!

a) How wide is th

Explanation / Answer

Part A)

Apply y/L = m(wavelength)/a

y/4 = (1)(640 X 10-9)/(3 X 10-6)

y = .853 m

The central max is twice that value...

That is 1.71 m

Part B)

y/L = m(wavelength)/d

.0275/4 = 3(640 X 10-9)/(d)

d = 2.79 X 10-4 m (279 um)

Part C)

tan(angle) = m(wavelength)/d

Calculate d

We have 239 total slits. There are 238 spaces, so 238(2.79 X 10-4) = .0665 m

d = .0665/239 = 2.78 X 10-4 m

tan(angle) = 3(640 X 10-9)/(2.78 X 10-4)

angle = .396o

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