A pair of narrow slits is positioned 2.00 m from a screen and illuminated with l

Question

A pair of narrow slits is positioned 2.00 m from a screen and illuminated with light made up of two wavelengths 604.00 nm and 512.60 nm.

First a filter is used to block the 512.60 nm light from reaching the screen.  The resulting interference maxima are found to be separated by s = 2.10 mm.

a) What is in meters the separation of the slits?

We now remove that filter and place a filter that blocks the 604.00 nm light.

b) What is in mm the obtained fringe separation?

We remove both filters.

c) What is in meters the separation on the screen of first bright maxima due to both wavelengths?

d) What is in meters the separation on the screen of fourth bright maxima due to both wavelengths?

Explanation / Answer

Part A)

Apply y/L = m(wavelength)/d

(.0021)/2 = 1(512.6 X 10-9)/d

d = 4.88 X 10-4 m

Part B)

y/2 = (604 X 10-9)/(4.88 X 10-4)

y = 2.47 mm

Part C)

(delta y) = m(delta wavelength)/d

delta y = 1(604 X 10-9 - 512.6 X 10-9)/(4.88 X 10-4)

delta y = 1.87 X 10-4 m

Part D)

delta y = 4(604 X 10-9 - 512.6 X 10-9)/(4.88 X 10-4)

delta y = 7.89 X 10-4 m

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