Displacement of Fringes, Fringes, Interference of Fringes, Interference of Light

Displacement of Fringes, Fringes, Interference of Fringes, Interference of Light

DISPLACEMENT OF FRINGES

If a thin glass or mica strip or any other transparent plate of uniform thickness is introduced in the path of one of the two interfering beam from two coherent sources then central bright fringe will be displaced. This displacement from C to C00 will towards the side of lamina.

In order to calculate the displace we shall find the path difference between two beam from coherent sources S1 and S2 at any point ‘P’ on the screen. Let ‘t’ be the thickness of sheet and ‘μ’ the refractive index of its materials.

Time T taken by the beam to reach from S1 to P is given by

where C is the velocity in air and V is velocity of light in the medium of the plate

The condition for maxima

If P is the centre of the nth bright fringe

Shift of Central Fringe

Shift of central bright fringe where n=0 is given by

This expression is independent of n. This indicate that all the bright fringes are displaced through the same amount equal to  similarly it can be shown that the displacement of any dark fringe is also

The fringe width ω is given by

Bragg's Law of Diffraction, Define Bragg's Law, Bragg's Law Derivation

Bragg's Law of Diffraction, Define Bragg's Law, Bragg's Law Derivation

BRAGG’S EQUATION FOR X-Ray DIFFRACTION

When monochromatic X-Rays are incident as a crystal they get scattered by the crystal atom Brag propounded a law the constructive diffraction which is called the Bragg’s Law.

According to Bragg’s Law if d is the separation between the two nearest plane and Q is the glancing angle of the incident X-Ray with the crystal plane then for the constructive diffraction.

Consider a crystal in which atoms are arranged in a periodic manner with interatomic spacing ‘d’. A narrow beam of monochromatic X-Ray of wavelength λ is allowed to fall on a crystal at a glancing angle θ. The crystal acts as a diffracting grating with atoms as the opaque part and the spacing between them as the transparent part.

Let AB and DE be the incident rays and BC and EF be the corresponding reflected rays the path difference between the rays ABC and DEF is (GE+EH) therefore the path difference is given by

Constructive interference takes place only when the path difference is equal to nλ that is when the following condition satisfied

Davisson-Germer Experiment, Principle of Davisson and Germer Experiment

Davisson-Germer Experiment, Principle of Davisson and Germer Experiment

DAVISSON AND GERMER EXPERIMENT

The experiment performed by Davisson and Germer confirmed the De-Broglie hypothesis by demonstrating that electron beams get diffracted when scattered by a crystal.

In this experiment, electrons emerge out of a hole in the form of a fine beam which is then made to fall on a nickel crystal. Electrons are scattered in all direction by the atom of the crystals. The intensity of the electrons scattered in a particular direction is found by detector. By rotating the detector about an axis the intensity of scattered beam can be measured for different angles.

Newton's Rings, Newton's Rings in Interference

Newton's Rings, Newton's Rings in Interference

NEWTON’S RINGS

When a plane-convex lens of large focal length is placed as a plane glass plate, A thin film of air is formed between the lower surface of the plate. The thickness of the air film is very small at the point of contact and gradually increased from the centre upwards. If a monochromatic light is allowed to fall normally on this film, a set of alternate dark and bright fringes will be seen in the film. The fringes are concentric circle with their centre dark. These circles or rings are called Newton Rings.

Newton Rings are formed as a result of interference between light wave reflected from the upper and lower surfaces of the air film.

 

Newton’s Rings by Reflected Light

Suppose the radius of curvature of the lens is R and the thickness of the air film I ‘t’ at a distance OQ=r, from the point of contact O. The effective path difference between the interfering rays is

For the bright fringes 

For μ=1 and for normal incidence r=0

So,

For the dark rings

It is clear that a bright or dark fringe of any order n depend upon the thickness of the air film. Since t is constant along a circle with its centre at the point of contact, the fringe are in the form of concentric circle.

Diameter of Bright Rings

Substituting the value of t in eqn. (2)

For bright rings

So from eqn. 5

Thus the diameters of bright rings are proportional to the square root of the odd number

The separations between successive rings are 0.732:0.504:0.410

Diameter of Dark Rings

From equation (3) and (4)

If D is the diameter of dark ring

Thus the diameters of dark ring are proportional to the square root of natural number

Clamper, Clamper Circuit, Diode Clamper Circuit, Clamper Electronics, Clamper Circuit Analysis

Clamper, Clamper Circuit, Diode Clamper Circuit, Clamper Electronics, Clamper Circuit Analysis

What is Clamper?

Clamper circuit fixes one extremity of a wave form to a certain voltage level regardless of changes in the input wave form. Thus in the clamper circuit the input and output signals have the same shape but different dc levels.

POSITIVE CLAMPER

Drawing output of Circuit Below: 

CLAMPER 1:

The input to the circuit is sine wave here.

In the first +ve cycle of the diode D is reverse bias.

During the first –ve cycle of the input the diode D is forward bias. Current in the circuit will flow from point B-D-C-A. This will charge capacitor C in the shown polarity to the peak input voltage (Vm). Applying KVL in –ve cycle.

Capacitor Voltage Vc is Vm.

Now Applying KVL in +ve cycle.

The circuit has a output in which the waveform is shifting up thus it is called Positive Clamper.

Drawing output of Circuit Below (Biased Clamper):

CLAMPER 2:

During +ve Cycle, Apply KVL

Drawing output of Circuit Below (Biased Clamper):

CLAMPER 3:

During –ve cycle

During +ve cycle

NEGATIVE CLAMPER

If we turn the diode, the polarity of capacitor voltage reverses and the circuit becomes negative Clamper.

Drawing output of Circuit Below:

CLAMPER 4:

Drawing output of Circuit Below (Biased Clamper):

CLAMPER 5:

During +ve cycle

Drawing output of Circuit Below (Biased Clamper):

CLAMPER 6:

To calculate Vc

To Calculate Vo

Clipper, Clipper Circuit, Diode Clipper Circuit, Clipper Electronics, Clipper Circuit Analysis

Clipper, Clipper Circuit, Diode Clipper Circuit, Clipper Electronics, Clipper Circuit Analysis:

DEFINITION OF CLIPPER

Clippers are wave shaping circuits in which diodes are used to clip or cut off one or both extremities from the wave form of input wave or pulse.

PARALLEL CLIPPER:

In this type of Clipper, Diodes are connected in parallel to the load.

DRAWING OUTPUT OF THE FOLLOWING CLIPPER CIRCUITS:

CLIPPER 1:

CLIPPER 2:

CLIPPER 3:

CLIPPER 4:

CLIPPER 5:

SERIES CLIPPER 

The Clipper Circuit in which Diode is in series with the load is called Series Clipper.

DRAWING OUTPUT OF THE FOLLOWING CLIPPER CIRCUITS:

CLIPPER 6:

CLIPPER 7:

CLIPPER 8:

CLIPPER 9:

1.       POSITIVE CLIPPER

The clipper circuit in which positive cycle of input gets clipped off is called Positive Clipper.

2.      NEGATIVE CLIPPER

The clipper circuit in which negative cycle of the input gets clipped off is called Negative Clipper.

3.      BIASED CLIPPER

Clipper circuit in which a portion of negative or positive cycle of input gets clipper off is called biased Clipper. In this type, a battery is also involved.