Embibe Experts Solutions for Chapter: Wave Optics, Exercise 3: Exercise-3

An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency $10 \mathrm{GHz}$. What is the frequency of the microwave measured by the observer? (speed of light$=3\times {10}^8{ \mathrm{m} \mathrm{s}}^{-1}$)

In Young’s double slit experiment, the slits are $2 \mathrm{mm}$ apart and are illuminated by photons of two wavelengths ${\mathrm{\lambda }}_1=12000 \mathrm{Å}$ and ${\mathrm{\lambda }}_2=10000Å$. At what minimum distance from the common central bright fringe on the screen $2 \mathrm{m}$ from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other?

A parallel beam of fast moving electrons is incident normally on a narrow slit. A fluorescent screen is placed at a large distance from the slit. If the speed of the electrons is increased, then which of the following statements is correct?

In a double-slit experiment, the two slits are $1 \mathrm{mm}$ apart and the screen is placed $1 \mathrm{m}$ away. A monochromatic light of wavelength $500 \mathrm{nm}$ is used. What will be the width of each slit for obtaining ten maxima of double-slit within the central maxima of single-slit pattern?

For a parallel beam of monochromatic light of wavelength $\lambda \text{'},$ diffraction is produced by a single slit whose width $\text{'}a\text{'}$ is of the wavelength of the light. If $\text{'}D\text{'}$ is the distance of the screen from the slit, the width of the central maxima will be

In a diffraction pattern due to a single slit of width $e$, the first minimum is observed at an angle $30°$ when light of wavelength $5000 \stackrel{\mathrm{o}}{\mathrm{A}}$ is incident on the slit. The first secondary is observed at an angle of:

A linear aperture whose width is $0.02 \mathrm{cm}$ is placed immediately in front of a lens of focal length $60 \mathrm{cm}$. The aperture is illuminated normally by a parallel beam of light of wavelength $5\times {10}^{-5} \mathrm{cm}$. The distance of the first dark band of the diffraction pattern from the centre of the screen is:

In Young's double slit experiment the separation $d$ between the slits is $2 \mathrm{mm},$ the wavelength $\lambda$ of the light used is$5896 \mathrm{\AA }$ and distance $D$ between the screen and slits is $100 \mathrm{cm}.$ It is found that the angular width of the fringes is $0.20^{\circ} .$ To increase the fringe angular width to $0.21^{\circ}$ (with same $\lambda$ and $D$ ) the separation between the slits needs to be changed to