To my understanding,in multi slit interference, 2 equations are correct. $n*\lambda=d*sin(\theta)$ and $S=(\lambda*D)/d$ In the problem below, however, the 2 equations gave different solutions. I hope to understand why that is.

The problem is below: enter image description here

Using the first equation $n*\lambda=d*sin(\theta)$, the answer I got was $1.51$. Specifically:

  • When we solve the equation for $\theta$ with $700$ nm, we get $22$ degrees. When we solve with $400$ nm, we get $12$ degrees. We then take the tangent of the 2 and multiply both by $8.13$, then subtract them. This is how we get $1.51$ m.

Using the second equation $S=(\lambda*D)/d$, the answer I got was $1.31$. Specifically:

  • I subbed the given values and $400$ nm into the equation, then did the same for $700$ nm. Then I multiplied the 2 results by $2$ (to get the distance from center to second principle maxima), then subtracted both.

So why would the 2 equations give different solutions?


I suspect that your second formula has $S$ as the fringe separation on a screen that is $D$ away from slits which are $d$ apart.
That being so the second formula can be derived from the first formula on the assumption that the angle $\theta$ is small such that $\tan \theta \approx \sin \theta \approx\theta$.
In your problem the approximation is not a very good one and that results in a difference between your two answers.

So you have something like $n \lambda = d \sin \theta_{\rm n} \Rightarrow n \lambda \approx d \,\dfrac {s_{\rm n}}{D}$ and $(n+1) \lambda = d \sin \theta_{\rm n+1} \Rightarrow (n+1) \lambda \approx d \,\dfrac {s_{\rm n+1}}{D}$.

Subtraction and rearrangement gives $s_{\rm n+1} - s_{\rm n} = S \approx \dfrac{\lambda D}{d}$


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.