Refraction by plane surface and slab

Here the  fig1  shows how rays diverging from a point  O placed in a denser medium, appear to come from lesser distant  point I , if viewed from  rarer medium.

If the point O is at distance d from the boundary AB, the distance of point I will be  d / m .

Fig 2 shows how the rays incident from rarer  medium and  tending to meet at a point O  in the denser medium, gets diverged at the plane boundary   and meet at a distant point I .

If the point O is at distance d from the boundary AB, the distance of point I will be   m d 


Now look at the two  situations shown below where a slab of denser medium is refraction the rays  which are incident from rarer medium. In first case, the rays are tending to converge at some point 

O but are diverged  away  to meet at point I after the refraction from both faces of the slab. This shift from O to I can be obtained as t (1-1/m )   where   t   is the thickness of the slab.

In the other case where the rays are diverging from  a point O, then after refraction by both faces of the  slab, the rays are further diverged and appear to come from  a point    I  which is at distance    t (1-1/m )  again from the point O.

So a  slab of denser medium acts as diverging system !

Telescope & Magnifying Power

Fig-1 shows a telescope in the normal adjustment i.e. when the final image is formed at infinity and the eye is most relaxed. In this situation , 

• the magnifying power of the  telescope will be numerically equal to  ratio of the focal length of the objective to the focal length of the eye piece i.e.   f₀ / f_e  .  Sign-wise, it will be negative as the final image is inverted with respect to the object.
• Separation between the objective and the eyepiece  ( also called length of the instrument) will be equal to the sum of the focal lengths of the two lenses i.e. objective and eyepiece.
• The  intermediate image is real and inverted.
• The overall magnifying power will be more in magnitude if the focal of the objective  is increased and focal length of the eyepiece is decreased.
•   If focal length of the objective is increased, the size of the intermediate image  grows in same proportion.

In the second fig, the telescope is so adjusted that the final image is positioned at the near point with respect to the eyepiece. In this situation 

• Magnifying power  will be of magnitude  ( f₀ / f_e ) (1+ f_e / D). This value of the magnifying power is more than that of in normal adjustment.
• Length of the instrument  is now  f_{0 +   (} f_e D )/ (f_e +D)  because the intermediate image  will now be at distance  f_e D / (f_e +D)  from the eyepiece. Note that this length is  shorter than the length in case of the normal adjustment.

For JEE MAINS :Telescopes

* It is very well known to most of the students, that astronomical telescope produces final image inverted with respect to the original object. So overall magnifying power is of negative sign.

*To overcome this defect, two telescopes have been proposed , one called  terrestial  telescope  and second one Galelian telescope. The terrestrial uses another converging lens placed between the objective and eyepiece . This lens simply inverts the intermediate image without numerically modifying  magnifying power.Introduction of this third converging lens increases the  length of the instrument by  4 F where F is the focal length of the third lend introduced between the objective and eyepiece.  This third  lens is so adjusted that the image  formed by the objective lies at the 2F point of the third lens to be introduced.

For JEE MAIN : Practice test on current and heat

link 

Chromatic aberration ..in lenses

It is known  that  focal length of a lens depends on the refractive index of the material of the lens. From the lens maker's  formula  it can be easily  concluded  that  for  greater refractive index  lenses have lesser focal length in the magnitude . It is also well known that violet color has maximum ref index and red least.  So a lens will have least focal length  ( in magnitude ) for violet and maximum for red. For others  follow the order in VIBGYOR.

So if an object is emitting white light the images of different color will be formed at different places. This is not desired and this defect is called chromatic aberration.
The numerical value of the chromatic aberration is defined as the separation  between the images of violet and red color .  Dispersive power  ω of a lens is defined as  the ratio of the difference between  the focal lengths of red and violet color to the mean focal length which is for yellow.

ω =( fr - fv )/ fy 

It can be proved that when lenses  ( say A  and B ) of opposite nature i.e. on convex and other concave are placed in contact , then the combination will act as non chromatic i.e.achromatic, if their mean focal lengths and the dispersive powers follow the  relation     ω_A/  ω_{B  =} - f_A / f_B.

_{The non chromatic ( achromatic)  combination of lenses of same nature can also be obtained if they are placed with separation  d  which satisfy the relation  :  d = (} ω_A f_B +  ω_B f_{A ) / (} ω_A+ω_{B )}

OPTICS and WAVES--concepts and problems for JEE mains-24 feb-14

Concept 1: जब भी लाइट  का reflection ऑप्टिकली denser माध्यम  से होता है  तब फेज अचानक pi से change  हो जाता है  यानि कि अचानक आधी  wavelength के बराबर  path में change आ जाता  किन्तु यदि रिफलेक्सन  rarer medium से हो तब अचानक कोई फेज नहीं बदलता है !

Concept 2-: When light moves in a medium other than air, while considering its interference with some other wave travelling in air, the actual path of the wave travelling the other medium is  not directly taken  but it is modified  to a value  which is  the product of the refractive index of the medium and the actual path.

Example- 

Let light ray falls normally on a plane slab of thickness t  and refractive index 1.5. The slab is placed in the air. The light is partly reflected and remaining part is refracted and goes to other face where it gain is partly reflected and comes back and finally interfere with the wave which was reflected at the first face only. Wavelength of the light is  y in air. What is the phase difference between the waves interfering after reflections  from the tow faces ?

Under what conduction destructive interference  takes place between the reflected lights ? 

ANS :  (2p / l) ( 3 t ) - p   will the net phase difference between the interfering waves 

So   we get 3t- l/2 = (odd) l/2 ; Placing different values of  odd we can get different  possible value of  t  for a given wavelength l.

For Jee mains and and AIPMT

Many a times it is asked that when a north (or)south pole of a magnet is placed on a horizontal board, where could be the neutral point I.e. the point where horizontal component of the earth,s magnetic field is cancelled by the horizontal magnetic field component of the other magnetic source . The following two figures may help in getting the answer. The first fig shows how the magnetic field lines surround a magnet. This clearly hints that when this magnet is placed on a horizontal board with north pole on the board, the horizontal component of the filed lines looks like those , drawn in the fig 2.

Maths For JEE mains... Vector 18 feb

LC Oscillations

LC Oscillations refers to a situation

• where a circuit contains capacitor and inductor only and charge on the capacitor and current in the circuit, keeps on oscillating harmonically with time.
• where if charge on the capacitor decreases ( in magnitude) with time then current in the circuit increases with time.
• where sum of electrostatic energy in the capacitor and magnetic energy in the inductor, remains constant.

The oscillation frequency of current or charge, depends on the product of the self inductance and capacitanceC in the circuit. If this product is more then the frequency of the oscillation will be lesser.

If the charge and current oscillates with the angular frequency w then the w is equal to the square root of the inverse of the term LC for the circuit. So if both L and C are doubled then the angular frequency will be halved.

The variation of the charge or current with time will be similar to the variation of the position and velocity respectively of a block performing shm while being connected to one end of a spring . Is

• If initially charge on the capacitor is maximum, then after time t , it will be proportional to cosine of wt and current will be proportional to sine of wt.
• If initially current is maximum, then after time t current will be proportional to cosine of wt and the charge will be proportional to sine of wt.

Following are the questions relating to a circuit, which contains only L and C :

1-In the circuit, at time t =0, current is found to be zero and after 2 microseconds, the current grows to it's maximum value. What is the value the term LC for this circuit?

2-In the circuit, at time t =0, current is found to be zero and after 2 microseconds, the current grows to it's maximum value. What is lest value of the time t , when energy stored in the inductor attains half of it's maximum value?

3-In the circuit, initially current is maximum and equals to 10 A. What will be the current when energy stored in the capacitor is three fourth of the total electromagnetic energy of the circuit?

4-In the circuit, initially energy stored in the capacitor and the inductor are same. If this happens again happens 4 microseconds later and never before, then what is the time period of oscillation of the current ?

5-Second derivative of charge with respect to time equals negative of 400 multiplied by the charge. What is the value of the expression LC for the circuit?

Viresh

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for 12th class physics :Practice test on electrostatic FIELD , POTENTIAL & ENERGY@viresh
Viresh Singh
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Viresh

Motional EMF

The following is description of a problem where loop is pulled in a magnetic region cutting the magnetic field lines. This article gives summary of the result relating to the variation of induced emf with time/ position

RC. Circuit dc source..

Gzb 01 Feb 14

1-In context of transistors, the coefficient hfe is same as beta .

2-In oscillators transistor operates in active mode as it works as amplifier there.

3-(a)In case of photoelectric experiment , if the power of the source is doubled and frequency of the light is also doubled, then saturation photoelectric current still remains unchanged.
3(b)In case of photoelectric experiment, if the source of light is a point source and it is moved to twice distance from the photoelectric plate, the saturation photoelectric current will decrease to one fourth but the stopping potential will remain same

4-In a series RLC ac circuit , quality factor

• decreases if resistance is increased
• decreases if the capacitance is increased
• increases if the self inductance is increased.

5-In series RLC ac circuit, the power factor

• Increases if the resistance increases
• may increase or decrease on increasing the self inductance depending on the value of the source frequency in comparison to the resonance frequency.

6-In hydrogen like atom, if the electron moves to higher energy level, it's kinetic energy decreases by same amount as the total energy increases.

7-In hydrogen like atom, deBroglie wavelength of the electron will be directly proportional to the principal quantum number of the orbit in which the electron is rotating.

8-Two magnets placed at large distance x from one another, exert force and torque on each other.
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9- In the above arrangements, in the first fig, the two magnets repel each other and apply clockwise torque on each other. In the second fig, the two magnets attract each other but will not exert torque. Note that the two magnets exert force on each other which vary as Fourth power of the inverse of their separation.

10-When light wave is reflected from an optically denser medium, it suffers phase change of 180 degree.

11- When a transparent sheet is pasted in front of any one slit in YDSE, then fringes move towards that slit , in this case fringe width remains unchanged but the order of a fringe at given location on the screen , changes by (n-1)t/ wavelength.

12-In amplifies with transistor operating in CE mode, output potential differs in phase by 180 degree with respect to input .

Viresh