$A$ Fraunhofer diffraction pattern due to a narrow slit is obtained on a screen placed at a distance $D$ from the slit whose slit width is $a$. The distance of the first secondary maximum from the central maximum is

$A$ light beam of wavelength $800 \,nm$ passes through a single slit and is projected on a screen kept at $5 \,m$ away from the slit. What should be the slit width for the ray optics approximation to be valid (in $\,mm$)?

For what distance is ray optics a good approximation when the aperture is $ 4 \,mm $ and the wavelength of light is $ 400 \,nm $ (in $\,m$)?

What is Fresnel distance? Write its formula.

Find the correct condition$(s)$ for Fraunhofer diffraction due to a single slit.

$A$ student is jogging on a straight path with a speed of $5.4 \,km/h$. Perpendicular to the path is a pipe with its opening $8 \,m$ from the road (see figure). The diameter of the pipe is $0.45 \,m$. At the other end of the pipe is a speaker emitting sound of $1280 \,Hz$ towards the opening of the pipe. As the student passes in front of the pipe,she hears the speaker sound for $T$ seconds. $T$ is in the range (Take speed of sound $= 320 \,m/s$):