^Clouds appears white
Hence when white light encounters obstacles of size a >> λ, all colours are scattered equally & resultant scatted light appears white. Due to this reason clouds appears white.
If the earth had no atmosphere, the sky would appear black and stars could be seen during day time also. In fact at a height of above 15 km, there is almost no air & the appears black.
^Sun appears red at Sun rise & sun set
This is because at Sun rise & sun set light passes through greater thickness of atmosphere, as a result more scattering takes place & blue colour & low wavelengths are scattered away by the scattering caused by the atmosphere & the colour which reaches us is unscattered red.
General scattering
When size of obstacles encountered by the light is much greater than the wavelength of light used, all wavelengths of light are scattered equally.
^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.
^Sky appears blue
As blue colour has least wavelength, hence when white light encounters obstacles of size a << λ, blue colour is scattered max. Due to this reason sky appears blue.
^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.
^Horizontal range
Horizontal distance in the plane of projection is called horizontal range, it is
Horizontal range is same for complementary angles.
The product of time of flights of two projectiles fired from same point with same speeds at complementary angles is
Vertical range
Diagram above shows a situation a projectile is fired at a speed u = 25 m/s. On changing the angle of projection its range and height changes. Note horizontal range is same for complimentary angles. Also vertical range is maxi if projection angle is maxi.
Facts
In going from O to A the following changes take place
Facts
vA = vB = vC and tA > tC > tB
2. Suppose a body projected vertically upwards from the top of tower of height ‘h’ reaches the ground in t1 second. If it is projected vertically downwards from the same top with same velocity, it reaches the ground in t2 seconds. If it is just dropped from the top, it reaches the ground in t second, then 
^Trajectory
Path traveled by a point particle is called trajectory (or locus). It is straight (if a & v are collinear) & curved otherwise.
^Instantaneous acceleration
Acceleration of a body is always in the direction of force acting on the body.
^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
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)
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