Your answer is off by a multiplicative factor.
Two lasers are shining on a double slit, with slit separation
\(d\)
. Laser one has a wavelength of \(\frac{d}{20}\)
, while laser two has a wavelength of \(\frac{d}{15}\)
. The lasers produce separate interference patterns on a screen a large distance L away from the slits.De eerste vraag was:
What is the distance
\(\Delta y\)
between the first maxima (on the same side of the central maximum) of the two patterns?En hierop had ik het goede antwoord:
Voor constructieve interferentie geldt
\(y_m=L\frac{m\lambda}{d}\)
met \(m\in\zz\)
.met hier m=1 (eerste maxima) en
\(\lambda_1=\frac{d}{20}\)
en \(\lambda_2=\frac{d}{15}\)
Dus \(\Delta y=y_2-y_1=\frac{L\lambda_1}{d}-\frac{L\lambda_2}{d}=L\left(\frac{1}{15}-\frac{1}{20}\right)=\frac{L}{60}\)
De tweede vraag:What is the distance between the second maximum of laser one and the third minimum of laser two, on the same side of the central maximum?
Voor destructieve interferentie geldt
\(y_m=L\frac{\left(m+\frac{1}{2}\right)\lambda}{d}\)
met \(m\in\zz\)
.Dan
\(y_1=\frac{Lm_1\lambda_1}{d}=\frac{L(2)(d/20)}{d}=\frac{L}{10}\)
met m=2 (tweede maximum)Dan
\(y_2=R\frac{\left(m_2+\frac{1}{2}\right)\lambda_2}{d}=\frac{L(7/2)(d/15)}{d}=\frac{7L}{30}\)
met m=3 (derde minimum).Oftewel
\(\Delta y=y_2-y_1=\frac{L}{10}-\frac{7L}{30}=\frac{2L}{15}\)
.Dit blijkt (schijnt) fout te zijn, want Your answer is off by a multiplicative factor.
Wie ziet de fout?
\\edit:
okee, eerste minimum correspondeert in de forumlule
\(y_m=L\frac{\left(m+\frac{1}{2}\right)\lambda}{d}\)
met m=0 in plaats van m=1. Dus derde minimum is m=2 ipv m=3.Dus dan zal het antwoord
\(\frac{L}{15}\)
moeten zijn 
\\edit2:
en dat is idd goed. Daar heb ik nou al meer dan 3 kwartier over na moeten denken
