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

$A$ converging lens of a telescope with a diameter of $5 \text{ cm}$ has a focal length of $25 \text{ cm}$. In the focal plane of the lens, the distance between the centres of the Fraunhofer diffraction pattern is (wavelength of light used = $5000 \text{ Å}$, Rayleigh's criterion is satisfied).

$A$ 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 $= 320 \,m/s$):

In the Fraunhofer diffraction experiment, $L$ is the distance between the screen and the obstacle, $b$ is the size of the obstacle, and $\lambda$ is the wavelength of the incident light. The general condition for the applicability of Fraunhofer diffraction is:

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

In a Fraunhofer diffraction pattern,the slit width is $0.2 \ mm$ and the screen is at $2 \ m$ away from the lens. If the distance between the first minimum on either side of the central maximum is $1 \ cm$,the wavelength of light used is: (in $Å$)