Law of Malus

If a linearly polarized light is incident on a Polaroid with the E-vector (electric field vector) parallel to the transmission axis, the light is completely transmitted by the Polaroid. If the E-vector (electric field vector) perpendicular to the transmission axis, the light is completely stopped by the Polaroid. If the E-vector (electric field vector) is at an angle θ to the transmission axis, the light is partially transmitted. The intensity of partially transmitted light (by the Polaroid) is

I = I₀cos²θ

Where
I0 is the intensity when the incident E-vector is parallel to the transmission axis.


(Polaroids have long chains of hydrocarbons which become conducting at optical frequencies. When light falls perpendicularly on the sheet, the electric field parallel to the chains is absorbed but the field perpendicular to the chains gets transmitted. The direction perpendicular to the chains is called the transmissiona axis of the Polaroid.

(Chapter Light waves)

Snell’s law

The law of refraction: the refracted ray lies in the plane of incidence.

Snell’ law is

n₁ sin θ₁ = n₂ sin θ₂

Where

n₁ and n₂ are the index of refraction of medium 1 and medium 2.
The index of refraction of a medium is the ratio between the speed of light c in vacuum and the speed of light v in that medium

n = c/v


θ₁, θ₂ are angles of incidence and angle of refraction in the medium 1 and medium 2.

(Chapter: Light waves)

Laws of friction

1. If the bodies slip over each other, the force of friction is given by

f_k = μ _kN

Where
f_k is the force of friction
N is the normal contact force
μ _k is the coefficient of friction between the surfaces

2. The direction of kinetic friction on a body is opposite to the velocity of this body with respect to the body applying the force of friction.

3. If the bodies do not slip over each other, the force of friction is given by

f_s = μ _sN

where

f_s = static force of friction
μ _s = coefficient of static friction between the bodies
N = normal force between them

The direction and magnitude of static friction are such that the condition of no slipping between the bodies is ensured.


4. The frictional force f_k or f_s does not depend on the areas of contact. It depends on normal contact force only.


(Chapter: friction)

Joules Laws Heating Due to Current in a Resistor

1. The heat produced in a given resistor in a given time is proportional to the square of the current in it

2. The heat produced in a given resistor by a given current is proportional to the timwe for which the current exists in it.

The heat produced in a given resistor by a given current in a given time proportional to its resistance

(Topic: thermal and chemical effects of electric current)

MaxWell's Speed Distribution Law

MaxWell's Speed Distribution Law

It is an equation giving the distribution of molecules in different speeds in a gas at a temperature.

If dN represents the number of molecules with speeds between v and v+dv then

dN = 4πN[m/2πkT]^3/2v²e^-mv²/2kTdv

where
dN represents the number of molecules with speeds between v and v+dv
N = total number of molecules in the gas
m = mass of a molecule
T = absolute temperature of the gas
v = velocity of the molecules

The speed v_p at which dN/dv is maximum is called the most probable speed.
Its value is given by

v_p = √(2kT/m)

(Topic: Kinetic theory of gases)

Laws of Thermodynamics

Zeroth law: If two bodies A and B are in thermal equilibrium and A and C are also in thermal equilibrium then B and C are also in thermal equilibrium.



First law of thermodynamics

∆U = ∆Q -∆W
Where
∆U = change in internal energy of a thermodynamic system
∆Q = Heat given to the system
∆W = work done by the system

Change in internal energy of a thermodynamic system is equal to the heat given to the system minus the work done by the system on surroundings or environment.

Second law of thermodynamics

Kelvin-Planck statement

It is not possible to design a heat engine which works in cyclic process and whose only result is to take heat from a body at a single temperature and convert it completely into mechanical work.


(Topic: Laws of Thermodynamics)

IIT JEE Physics Notes

I started my serious relearning effort in May 2007. The first post that I made in this blog was on 16th May 2007. I started the post with a prayer to Ganesha, and the project has progressed till now.

Now I can feel happy that I studied the JEE syllabus more or less fully and I am in a position to explain the various lessons to my child if she needs my help apart from her lectures at the Junior college and further lectures at IIT coaching class.
I started posting some points in the blogs to confirm to myself that I really studied various chapters. Fortunately, these notes are found to be useful by many others, judging by the visits to the blogs.

I presently started model problems blogs for each subject so that I go through some problems in each subject. While these blogs may not be comprehensive at this point of time, because I am not writing them with that objective, substantial amount of material is put into these blogs. I can definitely improve them to provide a more comprehensive material may be after July 2009.

IIT JEE Chemistry Notes
www.iit-jee-chemistry.blogspot.com

IIT JEE Mathematics Notes
www.iit-jee-maths.blogspot.com