The first diffraction minimum due to the single slit diffraction is seen at $\theta = 30^o$ for a light of wavelength $5000 \,\mathring{A}$ falling perpendicularly on the slit. The width of the slit is

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)?

The first diffraction minima due to a single slit diffraction is at $\theta = 30^o$ for a light of wavelength $5000 \,\mathring{A}$. The width of the slit is

The position of the direct image obtained at $O$,when a monochromatic beam of light is passed through a plane transmission grating at normal incidence,is shown in the figure. The diffracted images $A, B$,and $C$ correspond to the first,second,and third-order diffraction. When the source is replaced by another source of shorter wavelength,then:

Two slits are made $1 \; mm$ apart and the screen is placed $1 \; m$ away. What should the width of each slit be to obtain $10$ maxima of the double-slit pattern within the central maximum of the single-slit pattern (in $; mm$)? Blue-green light of wavelength $500 \; nm$ is used.

$A$ slit of width $d$ is illuminated by white light. The first minimum for red light $(\lambda = 6500\,\mathring{A})$ will fall at $\theta = 30^\circ$ when $d$ will be