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.
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?