# 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
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