H C Verma Solutions for Chapter: Light Waves, Exercise 4: EXERCISES

In a double slit interference experiment, the separation between the slits is $1.0 \mathrm{mm}$, the wavelength of light used is $5.0\times {10}^{-7} \mathrm{m}$ and the distance of the screen from the slits is $1.0 \mathrm{m}$.

$\left(a\right)$ Find the distance of the center of the first minimum from the center of the central maximum.

$\left(b\right)$ How many bright fringes are formed in one centimeter width on the screen?

In a Young's double slit experiment, two narrow vertical slits placed $0.800 \mathrm{mm}$ apart are illuminated by the same source of yellow light of wavelength $589 \mathrm{nm}.$ How far are the adjacent bright bands in the interference pattern observed on a screen $2.00 \mathrm{m}$ away?

Find the angular separation between the consecutive bright fringes in a Young's double slit experiment with blue-green light of wavelength $500 \mathrm{nm}.$ The separation between the slits is $2.0\times {10}^{-3} \mathrm{m}$.

A source emitting light of wavelengths $480 \mathrm{nm}$ and $600 \mathrm{nm}$ is used in a double slit interference experiment. The separation between the slits is $0.25 \mathrm{mm}$ and the interference is observed on a screen placed at $150 \mathrm{cm}$ from the slits. Find the linear separation between the first maximum (next to the central maximum) corresponding to the two wavelengths.

A white light is used in a Young's double-slit experiment. Find the minimum order of the violet fringe $(\mathrm{\lambda }=400 \mathrm{nm})$ which overlaps with a red fringe $(\mathrm{\lambda }=700 \mathrm{nm})$.

Find the thickness of a plate which will produce a change in optical path equal to half the wavelength $\lambda$ of the light passing through it normally. The refractive index of the plate is $\mu$.
 

A plate of thickness $t$ made of a material of refractive index $\mu$ is placed in front of one of the slits in a double slit experiment.

$\left(a\right)$ Find the change in the optical path due to introduction of the plate.

$\left(b\right)$ What should be the minimum thickness $t$ which will make the intensity at the center of the fringe pattern zero? Wavelength of the light used is $d$. Neglect any absorption of light in the plate.

A transparent paper (refractive index $=1.45$) of thickness $0.02 \mathrm{mm}$ is pasted on one of the slits of a Young's double slit experiment which uses monochromatic light of wavelength $620 \mathrm{nm}.$ How many fringes will cross through the center if the paper is removed?