^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.
^Time of flight
From point F.5. b (ii) we know vy = zero at
projectile reaches its maximum height from point of projection. In the absence of air friction, wind & upthrust (actually all forces other than gravity) projectile takes same time to return back from maximum height to level plane of projection i.e. to travel path OPMA will be twice of this time, the total time to travel path OPMA is called time of flight (T), thus
. Let a is the retardation due to air friction,
^Moving upstream & downstream
In such a case the boat is not crossing the river, rather it moves along or opposite to stream. Distance covered in the opposite to direction of river current is called upstream & that covered in the direction of river current downstream.
i.e. for a particular distance the still water time is the harmonic mean of upstream and downstream times.
^Average acceleration
^Linear momentum
The product of mass & linear velocity is called linear momentum, i.e. 
As mass is a positive scalar, thus linear momentum is always parallel to velocity.
^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
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