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Chapter 5: Q14E (page 1181)

Coherent light that contains two wavelengths, 660nm (red) and 470nm (blue), passes through two narrow slits that are separated by 0.300mm. Their interference pattern is observed on a screen 4.00m from the slits. What is the distance on the screen between the first-order bright fringes for the two wavelengths?

Short Answer

Expert verified

The distance on the screen between the first-order bright fringes for the two wavelengths is 2.53mm.

Step by step solution

01

Formula for the distance of the bright fringe

y=m位Rd

02

Determining the distance on the screen between the first-order bright fringes for the two wavelengths

Given: 位red=660nm=660*10-9m

位blue=470nm=470*10-9md=0.300mm=0.300*10-3mR=4.0mm=1

Assume that the angles of both lights are small, so the distance can be given as:

y=m位Rd

The distance between them can be given as:

鈭�y=yred-yblue

Plug the first formula into the last one,

鈭�y=m位redRd-m位blueRd鈭�y=mRd(位red-位blue)

Plug the given,

鈭�y=1.0*4.00.300*10-3(660*10-9-470*10-9)=2.53*10-3m=2.53mm

Thus, the distance on the screen between the first-order bright fringes for the two wavelengths is 2.53mm.

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