A pair of narrow, parallel slits separated by a distance of 0.284 mm are illumin

Question

A pair of narrow, parallel slits separated by a
distance of 0.284 mm are illuminated by the
green component from a mercury vapor lamp
of wavelength 545.3 nm. The interference
pattern is observed on a screen 1.46 m from
the plane of the parallel slits.
Find the distance from the central maximum
to the first bright region on either side
of the central maximum.
Answer in units of mm.
004 (part 2 of 2) 10.0 points
Find the distance between the first and second
dark bands in the interference pattern.
Answer in units of mm.

Explanation / Answer

a)

here by using

d = 0.284 mm = 0.284 * 10^-3 m

lambda = 545.3 * 10^-9 m

L = 1.46 m

then by using formula

delta y = (ybright at m =1 ) - (ybright at m = 0) = (lambda * L / d ) 1 - 0

delta y = lambda * L / d = 545.3 * 10^-9 * 1.46 / 0.284 * 10^-3

delta y = 2.803 mm

the distance from the central maximum to the first bright region on either side of the central maximum is 2.803 mm

b)

delta y =(ydark at m=1) - (ydark at m = 0)

delta y = [ (lambda *L/d )( 1 + 0.5 ) ] - [ (lambda *L / d) * ( 0+0.5)]

delta y = (3 * lambda *L / 2 *d ) - (lambda *L / 2 *d ) = lambda * L / d

therefore

delta y = lambda * L /d = 2.803 mm

the distance between the first and second dark bands in the interference pattern is 2.803 mm

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