Introduction to Wave Optics

Q.

Estimate the distance for which ray optics is good approximation for an aperture of 4 mm and wavelength 400 nm.

Q. The condition for observing Fraunhofer diffraction from a single slit is that, the wave front incident on the slit should be,

1. Spherical
2. Cylindrical
3. Plane
4. Elliptical

Q.

By Ray Optics, the phenomenon which can be explained is/are:

1. Refraction

2. Interference

3. Diffraction

4. Bending of light around obstacles

Q.

Determine the Fresnel distance if the aperture is of the size $1\mathrm{cm}$ and the wavelength is $500\mathrm{nm}$.

Q. A plane simple harmonic progressive wave of wavelength $120\text{cm}$ and speed $34800\text{cm/sec}$ is incident normally on a plane surface which is a perfect reflector of sound. Stationary waves are formed. The ratio of the amplitudes of vibration at points distant (i) $10\text{cm}$ and (ii) $30\text{cm}$ from the reflector is:

1. $1:2$
2. $1:0$
3. $1:1$
4. $1:4$

Q. In Davisson-Germer experiment, as shown below, where electrons are reflected from a crystal plane.


If at angle $i$, the peak diffraction is observed, the de Broglie wavelength of electrons can be calculated by

1. $d\sin i=n{\lambda }_B$
2. $2d\cos i=n\lambda$
3. $2d\sin i=n\lambda$
4. $d\cos i=n\lambda$

Q. what is the difference between ray optics and wave optics?

Q. For what distance is ray optics a good approximation when the aperture is $4mm$ and the wavelength of light is $400nm$?

1. $18m$
2. $30m$
3. $24m$
4. $40m$

Q. An aperture of size a is illuminated by a parallel beam of light of wavelength $\lambda$. The distance at which ray optics has a good approximation is

1. $\frac{a^2}{\lambda }$
2. $\frac{\lambda }{a}$
3. $\frac{\lambda }{a^2}$
4. $\frac{{\lambda }^2}{a}$
5. $a^2\lambda$

Q. The ratio of resolving power of an optical microscope for two wavelengths ${\lambda }_1=4000\AA$ and ${\lambda }_2=6000\AA$ is

1. 9:4
2. 3:2
3. 16:81
4. 8:27

Q. For what distance is ray optics a good approximation when the aperture is 4 mm wide and the wavelength is 500 nm?

1. 22 m
2. 32 m
3. 42 m
4. 52 m

Q. Light of wavelength 600 nm is incident on an aperture of size 2 mm. The distance upto which light can travel such that its spread is less than the size of the aperture is:

1. 12.13 m
2. 6.67 m
3. 3.33 m
4. 2.19 m

Q.

wat is aperture?

Q. Write about the main features in which the Fraunhofer and Fresnel approaches of diffraction differ.

Q. (a) Monochromatic light of wavelength 589 nm is incident from air on a water surface. If p for water is 1.33, find the wavelength, frequency and speed of the refracted light.
(b) A double convex lens is made of a glass of refractive index 1.55, with both faces of the same radius of curvature. Find the radius of curvature required, if the focal length is 20 cm.

Q. Sound waves with frequency $3000Hz$ and speed $343m/s$ diffract through the rectangular opening of a speaker cabinet and into a large auditorium of length $d=100m.$ The opening, which has a horizontal width of $30.0cm,$ faces a wall $100m$ away (Fig. 36-36). Along that wall, how far from the central axis will a listener be at the first diffraction minimum and thus have difficulty hearing the sound? (Neglect reflections.)

Q. Estimate how large can be the aperture opening to work with laws of ray optics using a monochromatic light of wavelength $450nm$ to a distance of around $20m$.

Q.

By Ray Optics, the phenomenon which can be explained is/are:

1. Refraction

2. Reflection

3. Bending of light through a tiny hole

4. Bending of light around obstacles

Q. The width of a plane incident wavefront is found to be doubled in a denser medium. If it makes an angle of ${70}^0$ with the surface, calculate the refractive index for the denser medium.

Q. Light guidance in an optical fibre can be understood by considering a structure comprising of thin solid glass cylinder of refractive index $n_1$ surrounded by a medium of lower refractive index $n_2$.
The light guidance in the structure takes place due to successive total internal reflections at the interface of the media $n_1$ and $n_2$ as shown in the figure. All rays with the angle of incidence $i$ less than a particular value $i_m$ are confined in the medium of refractive index $n_1$. The numerical aperture (NA) of the structure is defined as $\sin i_m$.

If two structures of same cross-sectional area, but different numerical apertures NA${}_1$ and $N{A}_2(N{A}_2<N{A}_1)$ are joined longitudinally, the numerical aperture of the combined structure is

1. $\frac{N{A}_{1}N{A}_2}{N{A}_1+N_2}$
2. $N{A}_1+N{A}_2$
3. $N{A}_1$
4. $N{A}_2$

Q. A plane wave of wavelength $590nm$ is incident on a slit with a width of $a=0.40mm.$ A thin converging lens of focal length $+70cm$ is placed between the slit and a viewing screen and focuses the light on the screen.
What is the distance on the screen from the center of the diffraction pattern to the first minimum?

Q. Light with wavelength $\lambda$ falls normally on a long rectangular slit of width $b$. Find the angular distribution of the intensity of light in case of Fraunhofer diffraction, as well as the angular position of the minima.

Q. In Fresnel diffraction, if the distance between the disc and the screen is decreased, the intensity of central bright spot will

1. increase
2. decrease
3. none of these
4. remain constant

Q. For a light of wavelength $800\text{nm}$, the limit of resolution of a telescope is found to be equal to $\alpha$. The limit of resolution for light of wavelength $400\text{nm}$ will be

1. $\frac{\alpha }{2}$
2. $\alpha$
3. $2\alpha$
4. $3\alpha$

Q. The source is at some distance from an obstacle. Distance between obstacle and the point of observation is $b$ and wavelength of light is $\lambda$. The distance of $n^{th}$ Fresnel Zone from the point of observation is :

1. $\frac{bn\lambda }{2}$
2. $b+\frac{n\lambda }{2}$
3. $b-\frac{n\lambda }{2}$
4. $b-n\lambda$