Interference of Light — Prelims Questions

In Young's Double Slit Experiment (YDSE), the distance between the slits is $0.5\text{ mm}$ and the screen is placed at a distance of $100\text{ cm}$ from the slits. If the wavelength of light used is $5000\text{ \AA}$, what is the fringe width?

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

In a 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 a YDSE, a thin transparent sheet of refractive index $1.5$ is placed in front of one of the slits. If the central bright fringe shifts by a distance equal to the width of 10 fringes, what is the thickness of the sheet? (Given: wavelength of light $\lambda = 6000\text{ \AA}$, $D=1\text{ m}$, $d=0.1\text{ mm}$)

Two coherent monochromatic light beams of intensities $I_1$ and $I_2$ interfere. The ratio of maximum to minimum intensity in the interference pattern is $25:9$. What is the ratio of their amplitudes?

Which of the following conditions is NOT necessary for sustained interference of light?