Light of wavelength $\lambda$ is incident on a slit of width $d$. The resulting diffraction pattern is observed on a screen at a distance $D$. The linear width of the principal maximum is then equal to the width of the slit if $D$ equals

In an experiment,electrons are made to pass through a narrow slit of width $'d'$ comparable to their de-Broglie wavelength. They are detected on a screen at a distance $'D'$ from the slit (see figure). Which of the following graphs can be expected to represent the number of electrons $'N'$ detected as a function of the detector position $'y'$ ($y = 0$ corresponds to the middle of the slit)?

In a single slit diffraction experiment, the first minimum for red light $(660 \ nm)$ coincides with the first secondary maximum of some other wavelength $\lambda$. The value of $\lambda$ is $..... \mathring{A}$.

Which of the following statements are correct with reference to single slit diffraction pattern?
$(I)$ The central maxima is twice as wide as the secondary maxima.
$(II)$ The intensity of secondary maxima decreases as we move away from the central maxima.
$(III)$ The width of the central maxima is independent of the slit width.
$(IV)$ The intensity of the central maxima is the same as that of the secondary maxima.

The condition for diffraction is

Red light of wavelength $6500 \, \mathring{A}$ is incident on a slit of width $0.50 \, \text{mm}$. Find the distance between the two first minima on both sides of the central maximum in the diffraction pattern. The distance between the screen and the slit is $1.8 \, \text{m}$.