Wave Optics Concept Page - 8

Formula

Fringe width in Fresnel biprism

ω=Dλd$\omega ={\displaystyle \frac{D\lambda }{d}}$,
where D$D$ is the distance between the imagined coherent sources and the screen of projection,
d$d$ is the length of the base of the prism.

Definition

Radius of central bright region

r0≈1.22λf2a=0.61λfa$r_0\approx {\displaystyle \frac{1.22\lambda f}{2a}}={\displaystyle \frac{0.61\lambda f}{a}}$
where f is the focal length of the lens and 2a is the diameter of the circular aperture or the diameter of the lens, whichever is smaller. Typically if λ≈0.5m,f≈20cm$\lambda \approx 0.5m,f\approx 20cm$ and a≈5cm$a\approx 5cm$, we have r0≈1.2μm$r_0\approx 1.2\mu m$

Diagram

Single slit experiment

NP−LP=asinθ≈aθ$NP-LP=asin\theta \approx a\theta$
θ≈λa$\theta \approx {\displaystyle \frac{\lambda }{a}}$
M2P=M1P=λ/2$M_{2}P=M_{1}P=\lambda /2$

Definition

Detection of Plane Polarised light by polaroid

When unpolarised light is seen through a single crystal (polaroid) intensity of transmitted light decreases, on account of polarisation, on rotating crystal, intensity of polarised light doesn't change.  Actually a combination of polariser and analyser helps in detection of plane polarised light.

Definition

Polarised and unpolarised light

Polarized light waves are light waves in which the vibrations occur in a single plane. Example: light coming out of a polaroid.
In unpolarised light  the oscillations of light waves are not all in a single direction.
Example : sunlight.

Law

Brewster's Law and Polarisation by reflection

When unpolarized light is incident on the boundary between two transparent media, the reflected light is polarized with its electric vector perpendicular to the plane of incidence when the refracted and reflected rays make a right angle with each other.
μ=siniBsinr=siniBsin(π2−iB)=taniB$\mu ={\displaystyle \frac{\sin i_B}{\sin r}}={\displaystyle \frac{\sin i_B}{\sin (\frac{\pi }{2}-i_B)}}=\tan i_B$

Definition

Partially polarized light

When unpolarized light hits a reflective surface, the vertically polarized aspects are refracted into the surface. The horizontally polarized aspects are reflected off the surface and the light is now perceived as partially polarized.

Example

Problem on Brewster's angle

Example: What is the Brewster angle for air to glass transition? (Refractive index of glass = 1.5.)

Solution:
μ=1.5$\mu =1.5$
Brewster angle is θ$\theta$ is given by:
tanθ=μ$tan\theta =\mu$
So, Brewster angle: θ=56.31o

BookMarks

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