Expression for fringe width in Young's Double Slit Experiment
Let S1 and S2 be two slits separated by a distance d.
GG' is the screen at a distance D from the slits S1 and S2.
Point C is equidistant from both of the slits.
The intensity of light will be maximum at this point because the path difference of the waves reaching this point will be zero.
At point P, the path difference between the rays coming from the slits is given by,
S1 = S2 P - S1 P
Now, S1 S2 = d, EF = d, and S2 F = D
For constructive interference, the path difference is an integral multiple of wavelengths, that is, path difference is n.
Graph of intensity distribution in young's double slit experiment is,
Three distinguishing features observed in Young's Double Slit experiment as compared to single slit diffraction pattern is,
1. In the interference pattern, all the bright fringes have the same intensity. The bright fringes are not of the same intensity in a diffraction pattern.
2. In interference pattern, the dark fringes have zero or small intensity so that the bright and dark fringes can be easily distinguished. While in diffraction pattern, all the dark fringes are not of zero intensity.
3. In interference pattern, the width of all fringes are almost the same, whereas in diffraction pattern, the fringes are of different widths.
Voltage of the source is given by,
V = Vo sin ωt
Let current of the source be I = Io sin ωt
Maximum voltage across R is VR = Vo R, represented along OX
Maximum voltage across L = VL = IO XL, represented along OY and is 90o ahead of Io.
Maximum voltage across C = VC = Io XC, represented along OC and is lagging behind Io by 90o
Hence, reactive voltage is VL - VC, represented by OB'
the vector sum of VR, VL and VC is resultant of OA and OB', represented along OK.
OK = Vo =
i.e., Vo =
Impedance, Z =
When, XL = XC , the voltage and current are in the same phase.
In such a situation, the circuit is known as non-inductive circuit.
Power factor, P1 = R/Z
The values displayed by Meeta and her father are:
Meeta: Curious mind
Meeta's Father: knowledge and patience
The answer that Meeta's father had given would be the advantages of using LED lights over a single bulb.
Advantages of LED:
a) LED's consume very less power as compared to an incandescent bulb.
b) The cost of tiny LED is much less than of a bulb. This reduces the maintenance cost of LED bulbs.
c) The working of the traffic will remain unhindered even if one of the bulbs is not working.
The tiny lights are called LED (Light Emitting Diode) and they work on the principle of de-excitation of electrons in a forward biased semiconductor upon passing electricity through them.
i) A transformer is a device that changes a low alternating voltage into a high alternating voltage or vice versa.
Transformer works on the principle of mutual induction.
A changing alternate current in primary coil produces a changing magnetic field, which induces a changing alternating current in secondary coil.
Energy losses in transformer:
Flux leakage due to poor structure of the core and air gaps in the core.
Loss of energy due to heat produced by the resistance of the windings.
Eddy currents due to alternating magnetic flux in the iron core, which leads to loss due to heating.
Hysteresis, frequent and periodic magnetisation and demagnetization of the core, leading to loss of energy due to heat.
a) Number of turns in secondary coil is given by,
b) Current in primary is given by,
If the angle of incidence is increased gradually, then the angle of deviation first decreases, attains a minimum value () and then again starts increasing.
Principale of potentiometer: The potential difference across any two points of current carrying wire, having uniform cross-sectional area and material, of the potentiometer is directly proportional to the length between the two points.
That is, V
V = IR = I
i.e., V =
For unifrom current and cross- sectional area, we have
E = 2 V; R = 15 ; RAB = 10
Potential difference across the wire, =
Therefore, potential gradient = 0.8/1 = 0.8 V/ m
Potential difference across AO =
Length, AO =
= ; which is the required balance length of the wire.
A reflecting telescope is as shown below:
In a reflecting telescope, an image is formed by reflection from a curved mirror. The image formed is then magnified by a secondary mirror.
Advantages of reflecting telescope over a refracting telescope are:
1. There is no chromatic aberration for reflecting telescopes as the objective is a mirror.
2. Spherical aberration is reduced in the case of reflecting telescopes by using mirror objective in the form of a paraboloid.
Drift velocity is the average velocity of the free electrons in the conductor with which they get drifted towards the positive end of the conductor under the influence of an external electric field.
Free electrons are in continuous random motion. They undergo changethey undergo change in direction at each collision and the thermal velocities are randomly distributef in all directions.
Electric field, E = -eE
Acceleration of each electron, ... (2)
m = mass of an electron
e = charge on an electron
Drift velocity is given by,
Electrons are accelerated because of the external electric field.
They move from one place to another and current is produced.
For small interval dt, we have
I dt = -q ; where q is the total charge flowing
Let, n be the free electrons per unit area. Then, total charge crossing area A in time dt is given by,
Idt = neAvd dt
Substituting the value of vd, we get
I.dt = neA
Current density, J =
From ohm's law, we have
Here, is the conductivity of the material through whic the current is flowing,
Alloys like constantan and manganin are used for making standard resistors because:
a) they have high value of resistivity
b) temperature coefficient of resistance is less.
Bohr's Quantisation Rule:
According to Bohr, an electron can revolve only in certain discrete, non-radiating orbits for which the total angular momentum of the revolving electron is an integral multiple of ; where h is the Planck's constant.
Using Rydberg's formula for spectra of hydrogen atom, we have
Hence, the relation between 3 wavelengths from the energy-level diagram is obtained.