Determine the angular separation between the central maximum and the first-order maxima of the diffraction pattern due to a single slit of width $0.25\, mm$ when light of wavelength $5890\,\mathring{A}$ is incident on it.

In a Fraunhofer diffraction experiment, a single slit of width $0.5 ~mm$ is illuminated by a monochromatic light of wavelength $600 ~nm$. The diffraction pattern is observed on a screen at a distance of $50 ~cm$ from the slit. What will be the linear separation of the first order minima (in $~mm$)?

In a single slit diffraction experiment,the width of the slit is doubled. Which one of the following statements is correct?

If $I_0$ is the intensity of the principal maximum in the single slit diffraction pattern,then what will be the intensity when the slit width is doubled?

If we observe the single slit Fraunhofer diffraction with wavelength $\lambda$ and slit width $e$,the width of the central maxima is $2\theta$. On decreasing the slit width for the same $\lambda$,what happens to $\theta$?

Answer the following questions:
$(a)$ In a single slit diffraction experiment, the width of the slit is made double the original width. How does this affect the size and intensity of the central diffraction band?
$(b)$ In what way is diffraction from each slit related to the interference pattern in a double-slit experiment?
$(c)$ When a tiny circular obstacle is placed in the path of light from a distant source, a bright spot is seen at the centre of the shadow of the obstacle. Explain why?
$(d)$ Two students are separated by a $7 \; m$ partition wall in a room $10 \; m$ high. If both light and sound waves can bend around obstacles, how is it that the students are unable to see each other even though they can converse easily?
$(e)$ Ray optics is based on the assumption that light travels in a straight line. Diffraction effects (observed when light propagates through small apertures/slits or around small obstacles) disprove this assumption. Yet the ray optics assumption is so commonly used in understanding location and several other properties of images in optical instruments. What is the justification?