Double Slit, different wavelengths change in X

[rss14]

Homework Statement

Two slits are 0.158mm apart. A mixture of red light (wavelength = 665nm) and yellow-green light (wavelength = 565nm) fall onto the slits. A screen is located 2.2m away. Find the distance between the third-order red fringe and the third-order yellow-green fringe.

Homework Equations

Since they ask for colored fringes, and not dark ones, it must be constructive interference.

x/L = (m*λ/ d)

x = 0.000158m
L = 2.2m
m = 3 (third order fringe)

λ of red = 6.65E-7m
λ of yellow-green = 5.65E-7m

The Attempt at a Solution

I did the equation twice, once for each wavelength.

For red I got x as 2.7E-2m, and for yellow-green i got x as 2.36E-2m.

The difference between these 2 values is 0.0034mm or 3.4mm.

The answer however, is supposed to be 28mm. . .


How was I supposed to do this?

 

[rss14]

Here is another question, similar concept.

Light of wavelengths 480nm and 632nm passes through two slits 0.52mm apart. How far apart are the second-order fringes on a screen 1.6m away?

 

[Redbelly98]

For red I got x as 2.7E-2m, and for yellow-green i got x as 2.36E-2m.

x for red is slightly off. Can you express the answer with one more decimal place of accuracy? I.e., 2.7_ e-2 m.

You're already in the right ballpark. I disagree with the 28 mm answer, who or what told you that is the answer?

 

[rss14]

The textbook says that in the back.

Also, the second question I posted has an answer of 7cm, according to the book.

 

[rss14]

I am going to bump this thread, hopefully my question will be answered before my test tomorrow.

 

[Redbelly98]

You have the correct approach, but you had some round-off error in the first problem.

Both book answers are wrong. For the 1st question, 28 mm is the displacement of the 665 nm, 3rd-order fringe, not the separation of the two colored fringes.

Not sure where they got 7 cm for the 2nd problem.

Good luck on the test.