Question

Two slits of width $a_1$ and $a_2$ are illuminated by light of same wavelength.The first diffraction minima produced by each of them are in directions inclined at angles ${\theta }_1$ and ${\theta }_2$. The ratio of $sin{\theta }_1$ to $sin{\theta }_2$ is

• A. $\frac{a_1}{a_2}$
• B. $\sqrt{\frac{a_1}{a_2}}$
• C. $\sqrt{\frac{a_2}{a_1}}$
• D. $\frac{a_2}{a_1}$

Answer 1

The correct option is D $\frac{a_2}{a_1}$

Given,

$d_1=a_1{d}_2=a_2$

We know that path difference is

$△x=n\lambda =dsin\theta$

Here wavelength n is constant therefore, $sin\theta$ is inversely proportional to $d$

$\frac{sin{\theta }_1}{sin{\theta }_2}=\frac{d_2}{d_1}$

$\frac{sin{\theta }_1}{sin{\theta }_2}=\frac{a_2}{a_1}$

Hence, correct option is D.