Question

Two identical narrow slits ${\text{S}}_1$ and ${\text{S}}_2$ are illuminated by light of wavelength $\lambda$ from a point source $\text{P}$ as shown in the figure. The light is then allowed to fall on a screen, and if $n$ is a positive integer, then the condition for destructive interference at $Q$ is-

• A. $(l_1-l_2)=(2n+1)\frac{\lambda }{2}$
• B. $(l_3-l_4)=(2n+1)\frac{\lambda }{2}$
• C. $(l_1+l_2)-(l_3+l_4)n\lambda$
• D. $(l_1+l_3)-(l_2+l_4)=(2n+1)\frac{\lambda }{2}$

Answer 1

The correct option is D $(l_1+l_3)-(l_2+l_4)=(2n+1)\frac{\lambda }{2}$

For the destructive interference,

$\text{Path difference}=\frac{(2n+1)\lambda }{2}$


$(l_1+l_3)-(l_2+l_4)=\frac{(2n+1)\lambda }{2}$
$\downarrow \downarrow \text{path by}\text{path by}{S}_1{S}_2$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(D\right)$ is the correct answer.