Question

The fraunhofer diffraction pattern of a single slit is formed at the focal plane of a lens of focal length $f$. The distance between $1^{st}$ and $2^{nd}$ maxima on screen is $y$ and $a$ is slit width. Then the wave length of light used is

• A. $\frac{ay}{3f}$
• B. $\frac{3f}{ya}$
• C. $\frac{2f}{ay}$
• D. $\frac{ay}{f}$

Answer 1

The correct option is D $\frac{ay}{f}$

For $n^{th}$ maxima, distance on screen from central maximum is $y_n=\frac{nf\lambda }{a}$
For $n=1$
$y_1=\frac{\lambda f}{a}$
For $n=2$
$y_2=\frac{2\lambda f}{a}$
$y=y_2-y_1=\frac{2\lambda f}{a}-\frac{\lambda f}{a}$
$y=\frac{\lambda f}{a}$
so $\lambda =\frac{ay}{f}$