^Dangers signals are made red
^Dangers signals are made red
Danger signals, traffic lights etc. are made red. Red light being longest wavelength is scattered least & hence can go to large distance without any appreciable loss due to scattering.
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^Scattering of light
^Scattering of light
When unpolarized light falls on a gas or air molecules light falling on air molecules. The electric field of light polarises the air molecule makes it an electric dipole, which starts oscillating under the influence of oscillatory electric field of light & these dipoles radiate electromagnetic waves in all directions. This process is called scattering of light & the radiated light is called scattered light, it is unpolarized & intensity is found to be strongest along a line perpendicular to the oscillation, & drops to zero along the line of oscillation. The amount of scattering depends on the obstacle size coming in its way e.g. dust particles, rain drops, ice particles etc. We have divided scattering in two type.
1. Rayleigh scattering
When size of obstacles encountered by the light is much smaller than the wavelength (a << λ) of light used, the amount of scattering is inversally proportional to the fourth power of the wavelength of light.
^Problem solving tips
^Problem solving tips
- If a particle is moving on a circular path with angular speed w about the center, then its angular speed about a point on the opposite side of the diameter passing through it is w/2.
- If uniform speed remains constant then the motion is called uniform circular motion. Magnitude of v, at & an respectively are
- On a rigid body all points undergo same angular displacement (θ) in same time interval thus all the points on a rigid body rotate at same angular speed (ω) & have angular acceleration (α), thus v, at & an ∝ r. Thus a point situated farthest from center circle will have maximum value of speed, tangential acceleration & normal acceleration. Also a point at center will have zero values of v, at & an.
is a unit vector directed radially or normally outwards. 
^For a body just released from a height
^For a body just released from a height
If a body is dropped from a height h,
1. it reaches the ground with speed 
[using v – s relation]
2. The time taken by it to reach the ground is 
[using s – t relation]
^Condition for shortest time
^Condition for shortest time
At a = 00 the time taken to cross the river will be minimum & given by 
This is the case when the boat w.r.t. water is moved along the normal to river current as shown below.
From the diagram one can write
^Brewster’s law
^Brewster’s law
Brewster discovered that when ordinary light is incident on the surface of a transparent medium the reflected light is partially plane polarized.
The extent of polarization depends on the angle of incidence. For a particular angle of incidence (called polarizing or Brewster angle (ip or p)
1. the reflected light is found to be completely polarized with its vibrations perpendicular to the plane of incidence.
2. the reflected & transmitted rays are perpendicular to each other, as shown in figure.
3. μ = tan p [called Brewster law
At i = p Ray 1: Incident ray (unpolarised)
Ray 2: Reflected ray (completely polarised)
Ray 3: Refracted ray (partially polarised)
For a ray incident form air to glass
aμg = 3/2, so p = tan-1 3/2 ⇒ p = 56.30
For a ray incident form air to water
aμw = 4/3, so p = tan-1 4/3 ⇒ p = 53.10
^Malus law
^Malus law
Let I0 be the intensity and ‘A’ the amplitude of the unpolarized light falling on the polarizer & θ be the angle between the pass axis of the polaroid & amplitude vector, then the component Acosθ, parallel to the pass axis (y) of polarizer passes through it & the component Asinθ, perpendicular to pass axis is blocked by the polarizer, thus the intensity of light transmitted by the polarizer is
I = k (A cosθ)2 = k A2 cos2 θ
or I = I0 cos2 θ [called Malus law
Actually the phase angle for a beam of unpolarised light can have any value from 00 to 3600. Now as the average value of cos2 θ for the range 00 to 3600 is 0.5, thus the average intensity of light transmitted by a polarizer is only 0.5 I0. Following observations can be explained on the basis of Malus law.
1. Two polarizes with parallel pass axis (y & y)
2. Two polarizes with crossed pass axis (y & z)
^Light through a polarizer
^Light through a polarizer
Let ordinary light propagating along +x axis falls normally on a tourmaline crystal having pass axis parallel to y axis as shown in the following diagram. On passing through the tourmaline crystal the electric field vibration parallel to pass axis are transmitted while the electric field vibration normal to pass axis are absorbed by the tourmaline.
^How do polarisers work
^How do polarisers work
A Polaroid is a thin commercial sheet containing long chain of hydrocarbons which become conducting at optical frequencies & absorb the electric field parallel to chains & transmit the electric field perpendicular to the chain length. This is why a direction perpendicular to the chain length is called the transmission axis or pass axis of the polarizer. For shown drawing y axis is pass axis.
^Polarisers
^Polarisers
Any device or material that plane polarizes the unpolarised light passed through it is called a polarizer. Nicol prism, Tourmaline crystal, Polaroid etc. are some commonly used Polarisers.
