# Double Slit, different wavelengths change in X

## 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?

## Answers and Replies

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
Staff Emeritus
Science Advisor
Homework Helper
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?

The textbook says that in the back.

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

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

Redbelly98
Staff Emeritus
Science Advisor
Homework Helper
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.