Young's Double Slit — Prelims Questions

In Young's Double Slit Experiment, the distance between the slits is $0.2\,\text{mm}$ and the screen is placed $1\,\text{m}$ away. The wavelength of light used is $500\,\text{nm}$. What is the fringe width?

In a YDSE setup, if the entire apparatus is immersed in water (refractive index $\mu = 4/3$), how does the fringe width change compared to when it's in air?

In YDSE, a thin transparent sheet of thickness 't' and refractive index '$\mu$' is placed in front of one of the slits. If the original central bright fringe was at $y=0$, what is the new position of the central bright fringe?

In YDSE, the intensity at the central maximum is $I_0$. What is the intensity at a point where the path difference is $\lambda/4$?

In YDSE, if the slit separation 'd' is doubled and the slit-to-screen distance 'D' is halved, what happens to the fringe width?

Which of the following conditions is NOT essential for observing a sustained interference pattern in Young's Double Slit Experiment?