Wave Optics Concept Page - 4

Definition

Fringes on the screen in Young's Experiment

In the double-slit experiment consecutive bright as well as dark fringes are observed on the screen as a consequence of type of interference.
The interference fringe maxima occurs for path difference = nλ$n\lambda$
The interference fringe minima occurs for path difference = (2n+1)λ$(2n+1)\lambda$

Definition

Describe Young's experiment to produce interference patterns

Young's Experiment:

If light consisted strictly of ordinary or classical particles, and these particles were fired in a straight line through a slit and allowed to strike a screen on the other side, we would expect to see a pattern corresponding to the size and shape of the slit. However, when this "single-slit experiment" is actually performed, the pattern on the screen is a diffraction pattern in which the light is spread out. The smaller the slit, the greater the angle of spread. The top portion of the image shows the central portion of the pattern formed when a red LASER illuminates a slit and, if one looks carefully, two faint side bands. More bands can be seen with a more highly refined apparatus. Diffraction explains the pattern as being the result of the interference of light waves from the slit.

Example

Solve problems on interference on a screen where a slab is introduced in front of a slit to create phase difference

Example: When a light wave passes from a rarer medium to a denser medium, there will be a phase change of π$\pi$ radians. This difference brings change in the conditions for constructive and destructive interference. This phenomena also reasons the formation of interference pattern in thin film like, oily layer, soap film, etc., but has no reason on the shifting of fringes from the central portion outward. The shift is dependent on the refractive index of the material as per the relation  Δy=(μ−1)t$\mathrm{\Delta }y=(\mu -1)t$.
On introducing a transparent slab(μ)$(\mu )$, the central fringe shifts to the point originally occupied by the fifth bright fringe. Find the thickness of the slab.

Solution:
Path difference between 5th bright fringe=5λ$5\lambda$
Path difference introduced due to insertion of a slab=t(μ−1)$t(\mu -1)$
Therefore, t(μ−1)=5λ$t(\mu -1)=5\lambda$
⟹t=5λμ−1$⟹t={\displaystyle \frac{5\lambda }{\mu -1}}$

Example

Problem on luminous intensity

Example: A lamp placed 60 cm$60cm$ from a screen produces the same illumination as a standard 100 W$100W$ lamp placed 90 cm$90cm$ away on the other side of the screen. Find the luminous intensity of the first lamp.

Solution:
For same illumination, Powerr2${\displaystyle \frac{Power}{r^2}}$ will be same
=> 1000.92=P0.62${\displaystyle \frac{100}{{0.9}^2}}={\displaystyle \frac{P}{{0.6}^2}}$
⇒$\Rightarrow$  P=44.44 W$P=44.44W$

Definition

Superposition principle

The superposition principle states that at a particular point in the medium, the resultant displacement produced by a number of waves is the vector sum of the displacement produced by each of the waves.

Definition

Coherent and Incoherent Sources

In coherent light the photons are all in 'step' other words the change of phase within the beam occurs for all the photons at the same time. There are no abrupt phase changes inside the beam. Light produced by lasers is both coherent and monochromatic (of one 'colour'). 

Incoherent source emits light with frequent and random change of phase between the photons. (Tungsten filament lamps and 'ordinary' fluorescent tubes emit incoherent light).

Definition

Coherent Sources

Coherent Sources: Two sources of light are said to be coherent if the waves emitted from them have the same frequency and are 'phase-linked', that is, they have a zero or constant phase difference.

Diagram

Interference Pattern for white light

BookMarks

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