Mechanical Engineering
1st Year 1st Semester
Course Name: Physics -II Course No: PHY 1131
Chapter 1: Interference, Newton’s ring
Physical Optics
1.
What is light? Explain briefly the nature of light.
i)
Quantum theory of light
ii)
Huygens wave theory of light
iii)
Electromagnetic theory of light
iv)
Newton’s corpuscular Theory of light
2. State the principal of superposition of light wave
Interference
1. What are coherent sources of light? Give the relation between phase difference and path
difference.
➢ Condition of Coherent source
2. What is meant by interference of light? Explain it with the necessary figure.
➢ Conditions for interference of light
➢ Explain the Young’s double slit experiment. (Derivation)
3. Give the relation between phase difference and path difference.
➢ Condition for constructive and destructive interference according to phase
difference
➢ Condition for constructive and destructive interference according to phase
difference
Mathematical Problems:
1. In a double slit experiment, if the distance between the slits is increased, how does it
affect the interference pattern on the screen?
2. Prove that the distance 𝛽 between two successive dark fringes is given by 𝛽 = 𝜆𝐷, where
𝑑
3.
4.
symbols have meaningful significant.
In Young’s experiment, the separation between two slits is 1 × 10−4 𝑚 and the distance
of the screen from the plane of slit is 0.50m. What is the distance from the central bright
point to the second bright point in the screen?
A narrow parallel slit of 1 mm apart is illuminated by monochromatic light. Fringes
formed on the screen held at a distance of 120 cm from the slits are 0.60 mm apart. Find
the wavelength of light.
5.
Two lights of wavelengths 560 nm and 420 nm are used in Young’s double slit
experiment. Find the least distance from the central fringe where the bright fringe of the
two wavelengths coincides. Give D=1m and d=3mm.
Newton’s Ring
1. Explain the formation of Newton’s rings and hence find an expression for the radius of
bright rings.
2. Describe the Newton’s ring experiment and explain how it is used to determine the
wavelength of Sodium light.
3. Describe how to form a newton’s ring by reflected ray of light with graphical
representation. Under what condition is the centre dark?
Mathematical Problem
1. Newton’s rings are formed with sodium light (𝜆 = 5.9 × 10−5 𝑐𝑚) between a plane glass
plate and a convex lens surface. The diameter of two successive dark rings are 2.0 𝑚𝑚
and 2.236 𝑚𝑚. What is the radius of curvature of the lens surface?
2. Newton’s ring is formed with sodium light (𝜆 = 5.9 × 10−5 𝑐𝑚) between a plane glass
plate and a convex lens surface. The diameter of two successive dark rings are 2.0 𝑚𝑚
and 2.236 𝑚𝑚. What is the radius of curvature of the lens surface?
3. In Newton’s ring experiment, the diameter of the 25th bright ring was to be 0.34 cm and
that of the 35th ring was 0.60 cm. If the sodium light (𝜆 = 5890Å) used as a source. Find
the radius of curvature of the plano-convex lens.
Diffraction
1.
2.
3.
Define plane diffraction grating. What is the difference between interference and
diffraction?
Distinguish between Fresnel and Fraunhofer classes of diffraction.
Or what do mean by Fraunhofer classes of diffraction?
Derive the conditions for minima and maxima for Fraunhofer diffraction at a single slit.
Mathematical Problems
1. A parallel beam of light wavelength 5460 Å is incident at an angle of 30° on a plane
2.
transmission grating which has 6000 lines/cm. Find the highest order spectrum that can
be observed.
In Fraunhofer diffraction due to a single slit, the screen is at a distance of 100 cm from
the slit and the slit is illuminated light of wavelength 5893Å. The width of slit is 0.1 mm.
Calculate the separation between the central maximum and the first secondary minimum.
3.
In a single slit diffraction pattern by red light (6000Å) gives first order diffraction
minima of 4° with axis. How wide is the slit?
Polarization
1.
2.
3.
4.
5.
Compare polarized and unpolarized light.
Explain the polarization of light?
➢ State Brewster’s law. Explain the production of polarization of light by reflection
and refraction.
➢ What was observation of the polarization of light by reflection given by
Brewster’s law?
➢ Show that at polarizing angle of incidence the reflected and refracted rays are
mutually perpendicular to each other.
Describe how Nichol prism polarizes the light.
➢ What is double refraction? Describe the characteristics of ordinary and extra
ordinary rays.
State and explain Mallus’s law.
➢ Explain the working principle of a polarimeter
Define optical activity?
➢ How is a polarimeter used to measure the strength of a sugar solution?
Mathematical Problem:
1. If light passes through a glass plate of refractive index 1.50, what will be the angle of
polarization and angle of refraction?
2. A 0.20 m long tube containing sugar solution rotates the plane of polarization by 11°. If
the specific rotation of sugar is 66°, calculate the strength of solution.
3. If the plane of vibration of the incident beam makes an angle of 30° with the optical
maxis compare the intensity of extraordinary and ordinary light.
Geometrical Optics
1.
2.
3.
4.
5.
What is quarter wave?
Explain the formation of an image of a point object by a convex mirror.
What are monochromatic and chromatic aberrations?
➢ Define aberrations and astigmatism.
➢ What do you understand by the term abberations? Explain its types.
Explain equivalent lens and equivalent focal length.
Derive the expression of focal length of a spherical surface.
6.
Prove that for a combination of two Coaxial thin Convergent lenses of focal lengths 𝑓1
and 𝑓2 , separated by a distance 𝑑 in air, the focal length 𝑓 of the combination is given by,
𝑓𝑓
1 2
𝑓 = 𝑓 +𝑓
−𝑑
1
7.
2
Two glasses have dispersive powers in the ratio 2 ⋮ 3. These glasses are to be used in the
manufacture of achromatic objective of focal length 20 cm. What are the focal lengths of
the lenses?
Oscillation
1.
2.
3.
4.
5.
6.
7.
Define damped, forced oscillations and resonance.
Explain simple harmonic motion and discuss its characteristics.
Derive the differential equation of simple harmonic oscillation.
Derive an equation for the potential energy of a particle executing SHM.
➢ Show that the total energy of a simple harmonic oscillator is proportional to the
square of its amplitude.
Explain damped harmonic motion with an example.
Obtain an expression for the displacement in the case of under damped oscillatory
motion.
Show that for a body vibrating simple harmonically the time period is given by
𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡
𝑇 = 2𝜋√
8.
𝐴𝑐𝑐𝑒𝑙𝑎𝑟𝑎𝑡𝑖𝑜𝑛
Define Lissajous figures.
➢ Calculate the result of two simple harmonic motions of equal time period when
they act at right angles to one another and when the phase difference is (ⅰ) 0, (ⅱ)
𝜋
2
and (ⅲ) 𝜋
➢ Derive a general expression for the resultant vibration of a particle of a
simultaneously acted upon two initially perpendicular simple harmonic
vibrations, having the same time period but different amplitudes and phases.
Mathematical Problem:
1. Calculate (ⅰ) the time period and (ⅱ) frequency of a simple harmonic motion represented
𝜋
by 𝑦 = 10 sin (10𝑡 − 6 ), where 𝑦 is measured in meters and 𝑡 in seconds.
2.
3.
Motion of a particle is given by 𝑥 = 5 sin 6.28𝑡 𝑐𝑚. Find the (ⅰ) displacement at 5 sec,
(ⅱ) velocity and acceleration of the particle at 5 sec.
The scale of a spring balance reading from 0 to 10 kg is 0.25 m long. A body suspended
10
2 from the balance is found oscillate vertically with frequency of 𝜋 hertz. Calculate the
mass of the body attached to the spring.
4.
6.
A particle of mass 3 gm is subjected to an elastic force of 48 𝑑𝑦𝑛𝑒 𝑐𝑚−1 and a damping
force of 12 𝑑𝑦𝑛𝑒 𝑐𝑚−1 sec. If the motion is oscillatory, find its period.
For the damped oscillator, 𝑚 = 250 𝑔, 𝑘 = 85 𝑁𝑚−1 and 𝑏 = 70 𝑔𝑠 −1 . (ⅰ) What is the
period of motion? (ⅱ) How long does it take for the amplitude of the damped oscillation
to drop to one-third of its initial value?
Waves
1.
2.
3.
Define wavelength, frequency and velocity of propagation in connection with wave
motion.
What are the differences between transverse and longitudinal waves?
What is progressive wave? Deduce an expression for the displacement 𝑦 of a particle at
a distance 𝑥 from the source at a time 𝑡.
➢ Derive an expression for a travelling wave.
4.
Derive the relation: 𝑑𝑡 2 = 𝑣 2 𝑑𝑥 2
6.
7.
8.
Prove that the energy of progressive wave, 𝐸 = 2𝜌𝜋 2 𝑓 2 𝑎2 𝜆.
Deduced an expression for the intensity of progressive wave.
What do you mean by phase velocity and group velocity?
➢ Distinguish between group and phase velocity.
9.
Show that the group velocity is given by relation: 𝑈 = 𝑣 − 𝜆 𝑑𝜆
𝑑2 𝑦
𝑑2 𝑦
𝑑𝑣
Mathematical Problems
1. If the frequency of a vibrating body is 600 𝐻𝑧 and the velocity of sound in air is 340 m/s,
find how far sound travels while the body completes 30 vibrations.
Sound Waves
1.
2.
3.
4.
5.
6.
What is meant by beat? Show that the number of beats per second is equal to the
difference in frequency of the two notes.
Write down the properties of standing /stationary wave and travelling wave.
Defined superposition of waves
Explain the interference of sound waves.
Discuss the mathematical formula of stationary/standing waves and hence defined nodes
and antinodes.
What is the resonance? What is the difference between beats and resonance?
Acoustics
1.
Explain Doppler’s principle.
➢ Discuss Doppler's effect in sound and obtain an expression for the apparent
frequency of the note when the source and listener are
(ⅰ) moving toward each other and
(ⅱ) moving away from each other
2. Derive an expression for change in frequency when the source is stationary and the
observer in motion.
➢ Derive an expression for change in frequency when the source in motion and the
observer is stationary
3. What are the requirements of an auditorium in an acoustic viewpoint?
4. Define reverberation time. Derive the expression of reverberation time using Sabine’s
theory.
5. Deduce an expression for the growth of sound intensity in a room.
6. Define audible, ultrasonic, infrasonic and supersonic waves.
7. Find an expression for the velocity of the sound wave in gas.
Mathematical Problem:
1. A person is standing on a railway's platform, an engine while approaching the platform
blows a whistle of pitch 660 hertz. The speed of the engine is 72 km/hr. The velocity of
sound is 350m/s, Calculate the apparent pitch of the whistle as heard by the person.
2.. Derive an expression for change in frequency 200 𝐻𝑧 is moving away from a stationary
observer and towards a rigid flat wall. The velocity of the car is 5 m/s. Calculate the
number of beats heard per second by the observer. Consider the velocity of the sound
wave in air is 350 m/s.
3. Two airplanes A and B are approaching each other with a speed of 360 km/hr. The
frequency of the whistle emitted by A is 1000 𝐻𝑧. Calculate the apparent frequency of
the whistle as heard by the passengers of airplane B. Velocity of sound in air= 350 m/s.
4. Calculate the velocity of the propagation of longitudinal wave in a steel rod
[𝑌𝑠𝑡 = 1.5 × 1012 𝑑𝑦𝑛𝑒𝑠 𝑐𝑚−2 ].