◆ Answer -

L = 7.5 cm

● Explanation -

# Given -

fo = +1.25 cm

fe = +5 cm

uo = -2.5 cm

ve = ∞

# Solution -

Applying lens formula for objective,

1/fo = 1/vo - 1/uo

1/1.25 = 1/vo - 1/-2.5

1/vo = 1/25 - 1/2.5

1/vo = 1/2.5

vo = 2.5 cm

Applying lens formula for eyepiece,

1/fe = 1/ve - 1/ue

1/5 = 1/∞ - 1/ue

1/5 = 0 - 1/ue

ue = -5 cm

Distance between the objective and eyepiece is -

L = |vo| + |ue|

L = |2.5| + |-5|

L = 2.5 + 5

L = 7.5 cm

Hence, distance between the objective and eyepiece is 7.5 cm.

Resistance has some fixed value like 100 Ω,10kΩΩ,10kΩ. On the other hand, Capacitive Reactance varies with the applied frequency, and hence any variation in supply frequency will have a big effect on the capacitive reactance value.

Torque is the measure of the force that can cause an object to rotate about an axis. Force is what causes an object to accelerate in linear kinematics. Similarly, torque is what causes an angular acceleration. Hence, torque can be defined as the rotational equivalent of linear force. The point where the object rotates is called the axis of rotation. In physics, torque is simply the tendency of a force to turn or twist. Different terminologies such as moment or moment of force are interchangeably used to describe torque.

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Let P be an axial point at distance r from the center of the dipole. Electric potential at point P is given as

V=V1+V 2

V1 and V 2

are the potentials at point P due to charges +q and –q respectively

V=1/ 4πε0( q/r−2a+(-q/ r+2a ))

V= 1/4πε0 ( 4a/(r²-4a²))

V= 1/4πε0(2P/(r²-4a²))

Hence, the electric potential is 1/4πε0 (2P/r²-4a²))

Consider, two charges q and -q seperated by distance 2a such that, it's total charge is 0.

 
Potential due to charge q = 
Potential due to charge -q =  
Potential due to dipole, is the sum of potential due to charges q and -q.
Therefore,
                    
 where, r₁ and r₂ are distances of charges q and -q from point P.

Now, 
 

Considering r much greater than a, r>>a.

Therefore,


Putting these values in the above equation of potential we have,

 

where, 

For potential at any point on axis,  
V= 

Potential is positive when  and potential is negative when  .

Electrical potential falls off at large distance, as  and not as characteristic of the potential due to a single charge.


 

Working Principle of Cyclotron

• A cyclotron accelerates a charged particle beam using a high frequency alternating voltage which is applied between two hollow “D”-shaped sheet metal electrodes known as the “dees” inside a vacuum chamber.
• The dees are placed face to face with a narrow gap between them, creating a cylindrical space within them for particles to move. Particles are injected into the center of this space.
• Dees are located between the poles of electromagnet which applies a static magnetic field B perpendicular to the electrode plane.
• The magnetic field causes the path of the particle to bend in a circle due to the Lorentz force perpendicular to their direction of motion.
• An alternating voltage of several thousand volts are applied between the dees. The voltage creates an oscillating electric field in the gap between the dees that accelerates the particles.
• The frequency of the voltage is set so that particles make one circuit during a single cycle of the voltage. To achieve this condition, the frequency must be set to particle’s cyclotron frequency.

1. The solid crystals are formed when the isolated atoms are brought together. Various interactions occur between the neighboring atoms.
2. At a particular interatomic spacing d, there is a proper balance between forces of attraction to form a crystal. In this process, the changes occur in the electron energy level configurations.
3. In case of a single atom, there is a single energy for an electron orbit.
4. However, when two atoms are brought close to each other, it leads to intermixing of electrons in the valence shell.
5. As a result, the number of permissible energy levels is formed, which is called an energy band.
6. Three bands are important from the conductivity point of view, which are,
7. Valence band
8. Conduction band
9. Forbidden gap or band
10. The simple energy band diagram, showing these bands is shown in the figure

1. In the normal state, the electrons involved in the covalent bonds in the crystal occupy the valence band and the conduction band is empty. Hence the electrons in the outermost shell are called valence electrons and the outermost shell is called valence shell.
2. At higher temperature, these electrons acquire energy and move to the conduction band as electron is not allowed to occupy any energy state in forbidden gap. These electrons are called free electrons.
3. For any given type of material the forbidden energy gap may be large, small or nonexistent. The classification of materials as insulators, conductors and semiconductors is mainly dependent on the widths of the forbidden energy gap.

Consider two points A and B separated by a small distance dx in an electric field.

Since dx is small, the electric field E is assumed to be uniform along AB. The force acting on a unit positive charge at A is equal to E.

Now, the work done in moving a unit positive charge from A to B against the electric field is dW=−E×dx.

The negative sign shows that the work is done against the direction of the field. Since the work done is equal to potential difference dV between A and B then dV=−E×dx or E=−dV​/dx

Thus, the electric field at a point is the negative of the potential gradient at that point.

N-Type Semiconductor

• Mainly due to electrons
• Entirely neutral
• I = I_h and n_h >> n_e
• Majority – Electrons and Minority – Holes

When a pure semiconductor (Silicon or Germanium) is doped by pentavalent impurity (P, As, Sb, Bi) then, four electrons out of five valence electrons bonds with the four electrons of Ge or Si.

The fifth electron of the dopant is set free. Thus the impurity atom donates a free electron for conduction in the lattice and is called “Donar“.

Since the number of free electron increases by the addition of an impurity, the negative charge carriers increase. Hence it is called n-type semiconductor.

Crystal as a whole is neutral, but the donor atom becomes an immobile positive ion. As conduction is due to a large number of free electrons, the electrons in the n-type semiconductor are the MAJORITY CARRIERS and holes are the MINORITY CARRIERS.

On July 7, HRD Minister Ramesh Pokhriyal announced a major CBSE syllabus reduction with 30% of the syllabus slashed for the year 2020-21 for classes 9 to 12 because of the reduction in classroom teaching time due to the Covid-19 pandemic and lockdown.

CBSE has rationalized the syllabus with the help of suggestions from NCERT and the same has been notified by a new CBSE notification as well.

The CBSE syllabus has been reduced but care has been taken so that the learning outcomes remain the same and the students do not miss out on learning core concepts in various subjects.

However, CBSE stated in its notification that though 30% of the syllabus has been cut from the new academic year, teachers should ensure that students understand these topics so that they can use the information in connection with other topics.

Deleted syllabus of CBSE Class 12 Physics

शांतनु महाभारत के एक प्रमुख पात्र हैं। वे हस्तिनापुर के महाराज प्रतीप के पुत्र थे। उनका विवाह गंगा से हुआ था। देवी गंगा ने इनके 7 पुत्रो को जन्म लेते ही अपने जल मे बहा दिया क्यों की वो श्राप से ग्रसित थे इस घटना से आहत हो कर इन्होंने गंगा को दिया वचन तोड़ दिया जिससे गंगा इन्हे छोड़ गयी जिससे उनका देवव्रत नाम का पुत्र हुआ। यही देवव्रत आगे चलकर महाभारत के प्रमुख पात्र भीष्म के नाम से जाने गए।

Electrostatic shielding is defined as a phenomenon that is seen when a Faraday cage is used to block the effects of an electric field. The effects of external fields on the internal contents are blocked using the cage.

The value of the angle between the vectors  and   

If  the monochromatic source is replaced by a source of white light, then there will be colourful interference fringes,consisting of seven colours.

The same thing we find in case of thin film of soap solution.

Below is the example where,White light incident on an oil film. A colorful interference pattern is observed when light from the sun is reflected from the top and bottom boundaries of a thin oil film.

Interference of Light

When two light waves of similar frequency having a zero or constant phase difference propagate in a medium simultaneously in the same direction, then due to their superposition maximum intensity is obtained at few points and minimum intensity at other few points.

This phenomena of redistribution of energy due to superposition of waves is called interference of light waves.

The interference taking place at points of maximum intensity is called constructive interference.

The interference taking place at points of minimum intensity is destructive interference.

Fringe Width

The distance between the centres of two consecutive bright or dark fringes is called the fringe width.

The angular fringe width is given by θ = λ / d.

where λ is the wavelength of light d is the distance between two coherent sources.

Young’s double slit experiment (YDSE)

The Young’s experiment shows that matter and energy can display both wave and particle characteristics.

Purpose of double slit experiment is as follows:-

1. In order to prove the wave nature of light.
2. To explain the phenomenon of interference.

Two coherent sources of light were taken in order to maintain the 0 or constant phase difference between the sources of light.

• Experimental set-up1:-
  • Young took an ordinary source of light(S) such as light bulb.
  • The light was made to pass through a very small slit S (which was comparable with the wavelength of light).
  • The light coming from Source S was made to pass through two small slits S₁ and S₂ which were separated by a very small distance d.
  • One screen was kept in front of these 2 sources.

Observation1:-

• He observed alternate dark and light bands were formed on the screen.

Setup 2:-

• Now he took 2 light bulbs i.e. 2 non coherent sources of light and placed a screen in front of them.

Observation 2:-

• He observed there were no alternate bands of light formed on the screen.
• Conclusion:-
• When coherent sources of light were taken then the phenomenon of interference is taking place.
• When non-coherent sources were taken phenomenon of interference was not taking place.
• The source S illuminated the sources S₁ and S₂ as a result the light from S₁ and S₂ become coherent.
• S was the source of bothS₁ and S_2, therefore if there is any change in the phase of the source there will be change in the both sources also.
• Therefore both S₁ and S₂ will be always in phase with each other.

Huygens Principle

• Huygens principle states that each point of a wavefront is the source of secondary wavelets (small waves) which spread in all directions with the speed of the wave.
• The new wavefront is formed by drawing a line tangent to all the wavelets.

For example:-

• If a stone is thrown in the river,waves will be formed surrounding that point.
• These waves look like concentric circles and they are known aswavefronts.
• The wavefronts gradually spread in all the directions.
• When the locus of all the waves is joined which are in the same phase, it will be the same as a sphere, and are known as Primary wavefront.
• Secondary wavefront are formed fromeach point on the Primary wavefront.
• The common tangential line that envelopes these secondary wavefronts will further give rise to other secondarywavefronts.
• All wavefronts will gradually fade after some time.

• Conclusion: - According to Huygens principle, every point on a wavefront give rise to secondary wavelets which spread out in all the directions with the speed of a wave.

Q : A converging lens of refractive index 1.5 is kept in a liquid medium having same refractive index. What would be the focal length of the lens in this medium?

A n s w e r :

The focal length of lens in a liquid-medium is given by

i.e., focal length of converging lens is infinity i.e., glass lens behaves as a glass plate.

Gauss"s Theorem: It states that net electric flux diverging normally from a closed surface is equal to 1/ε₀ times the net charge enclosed by the surface.

Let electric charge be uniformly distributed over the surface of a thin, non-conducting infinite sheet. Let the surface charge density(i.e., charge per unit surface area) be . We have to calculate the electric field strength at any point distant r from the sheet of charge. To calculate the electric field strength near the sheet, we now consider a cylindrical Gaussian surface bounded by two plane faces A and B lying on the opposite sides and parallel to the charged sheet and the cylindrical surface perpendicular to the sheet (fig) By symmetry the electric field strength at every point on the flat surface is the same and its direction is normal outwards at the points on the two plans surface and parallel to the curved surface.

Total electric flux