Wave Optics Concept Page - 8

Formula
Fringe width in Fresnel biprism
ω=Dλd,
where D is the distance between the imagined coherent sources and the screen of projection,
d is the length of the base of the prism.
Definition
Radius of central bright region
r01.22λf2a=0.61λfa
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 λ0.5m,f20cm and a5cm, we have r01.2μm
Diagram
Single slit experiment
NPLP=asinθaθ
θλa
M2P=M1P=λ/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(π2iB)=taniB
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
Brewster angle is θ is given by:
tanθ=μ
So, Brewster angle: 

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