Consider the Young’s Double Slit Experiment arrangement shown in figure. If d=10λ then position of 8th order maxima is y=p3D . Find the value of p.

# Consider the Young’s Double Slit Experiment arrangement shown in figure. If $d=10\lambda$ then position of ${\text{8}}^{\text{th}}$ order maxima is $y=\frac{p}{3}D$ . Find the value of $p$.

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### Solution:

Given
Distance between two slits $=10\lambda$
For maxima  $d\mathrm{sin}\text{θ}=n\lambda$

$\begin{array}{l}\mathrm{sin}\text{θ}=\frac{n\lambda }{d}=\frac{8\lambda }{10\lambda }⇒\mathrm{sin}\text{θ}=\frac{4}{5}⇒\mathrm{tan}\text{θ}=\frac{4}{3}\\ \text{Also }\mathrm{tan}\text{θ}=\frac{y}{D}\\ \therefore y=\frac{4D}{3}\end{array}$

Therefore, $p=4$

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