Interference of Light Waves and Young's Experiment

As you have learnt in the text, the principle of linear superposition of wave displacement is basic to understanding intensity distributions in diffraction and interference patterns. What is the justification of this principle?

In a double-slit experiment the angular width of a fringe is found to be $0.2°$ on a screen placed $1 \mathrm{m}$ away. The wavelength of light used is $600 \mathrm{nm}$. What will be the angular width of the fringe if the entire experimental apparatus is immersed in water? Take refractive index of water to be $\frac{4}{3}$.

A beam of light consisting of two wavelengths, $650 \mathrm{nm}$ and $520 \mathrm{nm}$, is used to obtain interference fringes in a Young’s double-slit experiment. What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide?

A beam of light consisting of two wavelengths, $650 \mathrm{nm}$ and $520 \mathrm{nm}$, is used to obtain interference fringes in a Young’s double-slit experiment. Find the distance of the third bright fringe on the screen from the central maximum for wavelength $650 \mathrm{nm}$.

In deriving the single slit diffraction pattern, it was stated that the intensity is zero at angles of $n\frac{\lambda }{a}$. Justify this by suitably dividing the slit to bring out the cancellation.

When a low flying aircraft passes overhead, we sometimes notice a slight shaking of the picture on our TV screen. Suggest a possible explanation.

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?

In double-slit experiment using light of wavelength $600 \mathrm{nm}$, the angular width of a fringe formed on a distant screen is $0.1°$. What is the spacing between the two slits?

Explain how Corpuscular theory predicts the speed of light in a medium, say, water, to be greater than the speed of light in vacuum. Is the prediction confirmed by experimental determination of the speed of light in water? If not, which alternative picture of light is consistent with experiment?

Estimate the distance for which ray optics is good approximation for an aperture of $4 \mathrm{m}\mathrm{m}$ and wavelength $400 \mathrm{n}\mathrm{m}$.

In Young’s double-slit experiment using monochromatic light of wavelength $\lambda$, the intensity of light at a point on the screen where path difference is $\lambda$, is $K$ units. What is the intensity of light at a point where path difference is $\frac{\lambda }{3}$?

In Young’s double-slit experiment, the slits are separated by $0.28 \mathrm{m}\mathrm{m}$ and the screen is placed $1.4 \mathrm{m}$ away. The distance between the central bright fringe and the fourth bright fringe is measured to be $1.2 \mathrm{c}\mathrm{m}$. Determine the wavelength of light used in the experiment.