When the distance of separation between the slit and screen is doubled, the angular separation between fringes in single slit diffraction pattern experiment

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)?

If $\lambda = 6000 \, \mathring{A}$ and $a = 18 \times 10^{-5} \, \text{cm}$,find the angular width of the central maximum in degrees $(^\circ)$.

$A$ plane wavefront of monochromatic light is incident normally on a narrow slit. $A$ diffraction pattern is formed on a screen. What is the phase difference between the waves originating from the top and bottom edges of the slit at the position of the first minimum?

Which scientist discovered the phenomenon of diffraction of light?

In the diffraction pattern, the first maximum is at $30^{\circ}$, when a monochromatic light of wavelength $\lambda$ is incident on a slit of width $a$. For the same wavelength, if the slit width is changed, so that the first maximum is at $45^{\circ}$, by how much is the slit width changed?