Quasi-Monochromatic Light and Young's Double Slit Experiment

[whoareyou]

Homework Statement

A quasi-monochromatic beam of light illuminates Young's double-slit setup, generating a fringe pattern having 5.6-mm separation between consecutive dark bands. The distance between the place containing the apertures and the plane of observation is 7 m, and the two slits are separated by 1.0 mm. What is the wavelength of the light?

Homework Equations

$y_m = (m+1/2)\lambda L / a$ (for destructive interference)

The Attempt at a Solution

$\lambda = \frac {y_m a}{(m+1/2)L}$

Since the separation between consecutive dark bands is 5.6 mm, then we can say that the distance to the first minimum (corresponding to $m=0$) is $5.6/2$. Then we have $a=1$ and $L=7000$ and the formula gives $\lambda=800 nm$ but the answer is supposed to be 560 nm. What am I doing wrong?

 

[ehild]

Then we have $a=1$ and $L=7000$ and the formula gives $\lambda=800 nm$ but the answer is supposed to be 560 nm. What am I doing wrong?

Nothing, your result is correct.

 

[rude man]

Agreed with post #2.