All Important Formula — Class 11 Physics Notes

All Important Formula · Class 11 Physics · 4 topics.

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Topics covered in All Important Formula

1.Optics
1. Snell's Law for Refractive Index
μ1μ2=sin⁡isin⁡r
Example:
A light ray travels from air (μ1=1) to water (μ2=1.33). If the angle of incidence i is 30∘, find the angle of refraction r.

Solution:
11.33=sin⁡30∘sin⁡r

0.752=0.5sin⁡r

sin⁡r=0.50.752=0.665

r=sin⁡−1(0.665)≈41.8∘
2. Brewster's Law
μ=tan⁡p(p = Angle of polarization)

Example:
If the angle of polarization p is 56∘, find the refractive index μ.

Solution:
μ=tan⁡56∘≈1.48
3. Relation Between Refractive Indices
n12×n21=1

n21=1n12
Example:
If n12=1.5, find n21.

Solution:
n21=11.5=0.67
4. Refractive Index Formula
μ=sin⁡isin⁡r
Example:
A light ray travels from air to glass with an incidence angle of 45∘ and a refraction angle of 28∘. Find the refractive index of glass.

Solution:
μ=sin⁡45∘sin⁡28∘=0.7070.469≈1.51
5. Mirror Formula
1f=1v+1u
Example:
An object is placed 20 cm in front of a concave mirror with a focal length of 10 cm. Find the image distance v.

Solution:
1−10=1v+1−20

1v=1−10+120=−2+120=−120

v=−20 cm
6. Lens Maker Formula
- In a Medium:
  1f=(μ−1)(1R1−1R2)
- In Air:
  1f=(μ−1)(1R1−1R2)
Example:
For a lens with μ=1.5, R1=20 cm and R2=−30 cm, find the focal length f.

Solution:
1f=(1.5−1)(120−1−30)
1f=0.5(120+130)
1f=0.5(3+260)=0.5×560=5120

f=24 cm
7. Equivalent Focal Length for Two Focal Lengths f1 and f2
1F=1f1+1f2
Example:
Two lenses have focal lengths f1=10 cm and f2=20 cm. Find the equivalent focal length F.

Solution:
1F=110+120=2+120=320

F=203≈6.67 cm
8. Power of a Lens
P=100f(in cm)
Example:
If the focal length of a lens is 25 cm, find its power.
Solution:
P=10025=4 diopters
9. Refraction Through Prism
μ=sin⁡(A+Dm2)sin⁡(A2)
Example:
If the refractive angle A=60∘ and the angle of minimum deviation Dm=40∘, find the refractive index μ.

Solution:
μ=sin⁡(60∘+40∘2)sin⁡(60∘2)μ=sin⁡50∘sin⁡30∘μ=0.7660.5=1.532
2.Oscillation Formulas
1. Differential Equation for SHM
d2xdt2+ω2x=0
Explanation:
This represents the equation of simple harmonic motion (SHM).

Example:
If ω=3 rad/s, the equation becomes:
d2xdt2+32x=0ord2xdt2+9x=0
2. Velocity in SHM
V=±ωA2−x2
Explanation:
This gives the velocity at a displacement x.

Example:
If ω=4 rad/s, A=5 m, and x=3 m:
V=±452−32=±425−9=±416=±16 m/s
3. Maximum Velocity (Vmax)
Vmax=ωA

Explanation:
This is the highest velocity the particle achieves.

Example:
If ω=6 rad/s and A=2 m:
Vmax=6×2=12 m/s
4. Acceleration in SHM
a=−ω2x
Explanation:
The acceleration is proportional to the displacement but in the opposite direction.

Example:
If ω=5 rad/s and x=2 m:
a=−52×2=−25×2=−50 m/s2
5. Displacement in SHM
x=Asin⁡(ωt±ϕ)
Explanation:
The position of the particle as a function of time.

Example:
If A=3 m, ω=2 rad/s, and ϕ=0, at t=1 s:
x=3sin⁡(2×1)=3sin⁡2≈3×0.909=2.727 m
6. Time Period for SHM
T=2πω
Explanation:
Time for one complete oscillation.

Example:
If ω=2 rad/s:
T=2π2=π≈3.14 s
7. Angular Frequency (ω)
ω=2πT
Example:
If T=4 s:
ω=2π4=π2≈1.57 rad/s
8. Potential Energy (P.E.)
P.E.=12mω2x2=12kx2
Example:
If m=1 kg, ω=3 rad/s, and x=2 m:
P.E.=12×1×32×22=12×9×4=18 J
9. Kinetic Energy (K.E.)
K.E.=12mω2(A2−x2)
Example:
If m=2 kg, ω=4 rad/s, A=3 m, x=1 m:
K.E.=12×2×42×(32−12)=1×16×(9−1)=128 J
10. Total Energy (T.E.)
T.E.=12mω2A2=12kA2
Example:
If m=1 kg, ω=5 rad/s, and A=2 m:
T.E.=12×1×52×22=12×25×4=50 J
11. Time Period of a Simple Pendulum
T=2πlg
Example:
If l=1 m and g=9.8 m/s2:
T=2π19.8≈2π×0.319=2.006 s
12. Time Period for a Mass-Spring System
T=2πmk
Example:
If m=2 kg and k=8 N/m:
T=2π28=2π0.25=2π×0.5≈3.14 s
13. Frequency (f)
f=1T
Example:
If T=2 s:
f=12=0.5 Hz
3.Gravitation Formulas and Constant Values of Physical Quantities
Gravitation Formulas

1. Newton’s Law of Gravitation
F=GMmr2
- Explanation:
  
  The gravitational force between two masses M and m separated by distance r.
- Example:
  If M=10 kg, m=5 kg, r=2 m, and G=6.67×10−11 Nm2/kg2:
  
  F=6.67×10−11×10×522=6.67×10−11×504=8.34×10−10 N
2. Gravitational Constant
G=6.67×10−11 Nm2/kg2
- Explanation:
  
  Universal constant used in the calculation of gravitational force.
3. Acceleration Due to Gravity (g)
g=GMR2
- Explanation:
  
  The acceleration due to gravity on the surface of a planet of mass M and radius R.
- Example:
  
  If M=5.98×1024 kg and R=6.37×106 m:
  
  g=6.67×10−11×5.98×1024(6.37×106)2≈9.8 m/s2
4. Gravitational Potential Energy
U=−GMmr
- Explanation:
  
  The potential energy between two masses M and m separated by distance r.
- Example:
  
  If M=10 kg, m=5 kg, r=2 m:
  U=−6.67×10−11×10×52=−1.67×10−9 J
5. Orbital Velocity (v0)
v0=GMr
- Explanation:
  
  The velocity required to keep a body in a circular orbit around a planet.
- Example:
  
  If M=5.98×1024 kg and r=6.37×106 m:
  
  v0=6.67×10−11×5.98×10246.37×106≈7.9 km/s
6. Escape Velocity (ve)
ve=2GMR
- Explanation:
  
  The minimum velocity needed to escape the gravitational pull of a planet.
- Example:
  
  For Earth, if M=5.98×1024 kg and R=6.37×106 m:
  
  ve=2×6.67×10−11×5.98×10246.37×106≈11.2 km/s
7. Time Period of a Satellite (T)
T=2πr3GM
- Explanation:
  
  The time taken for one complete revolution of a satellite around a planet.
8. Kepler’s Third Law
T2∝r3
- Explanation:
  
  The square of the time period of a planet’s orbit is proportional to the cube of the semi-major axis of the orbit.
9. Weight on a Planet (W)
W=mg
- Explanation:
  
  The weight of an object is the force due to gravity acting on it.
Constant Values of Physical Quantities
1. Velocity of Light (c)
  3×108 m/s
2. Gravitational Constant (G)
  6.67×10−11 Nm2/kg
  
  2
3. Acceleration Due to Gravity on Earth (g)
  9.8 m/s
  
  2
4. Planck’s Constant (h)
  6.63×10−34 Js
5. Avogadro’s Number (NA)
  6.022×1023 mol
  
  −1
6. Boltzmann Constant (k)
  1.38×10−23 J/K
7. Universal Gas Constant (R)
  8.314 J/mol\K
8. Electron Charge (e)
  1.6×10−19 C
9. Mass of Electron
  9.11×10−31 kg
10. Mass of Proton
  1.67×10−27 kg
11. Permittivity of Free Space (ϵ0)
  8.85×10−12 C2/Nm2
12. Permeability of Free Space (μ0)
  4π×10−7 Tm/A
13. Stefan-Boltzmann Constant (σ)
  5.67×10−8 W/m2K4
14. Gas Density of Air
  1.29 kg/m3
15. Speed of Sound in Air
  343 m/s
4.Electromagnetic Induction Formula
1. Faraday's Law of Induction
Formula:

ε=−dϕdt

Explanation:
The induced EMF (ε) is proportional to the rate of change of magnetic flux (ϕ) through a circuit. The negative sign follows Lenz's Law.

Example:
If the magnetic flux changes by 0.2 Wb in 0.1 s, the induced EMF is:

ε=−0.20.1=−2 V
2. Magnetic Flux

Formula:
ϕ=B⋅A⋅cos⁡θ

Explanation:
Magnetic flux (ϕ) depends on the magnetic field (B), area (A), and the angle (θ) between the field lines and the normal to the surface.

Example:
If B=5 T, A=0.1 m2, and θ=30∘:
ϕ=5×0.1×cos⁡30∘=0.5×0.866=0.433 Wb
3. Induced EMF in a Loop

Formula:
ε=−Ndϕdt

Explanation:
If a coil with N turns experiences a changing magnetic flux, the induced EMF is proportional to N and the rate of change of flux.
4. Induced EMF for a Moving Conductor

Formula:
ε=Bℓvsin⁡θ

Explanation:
The EMF induced in a conductor of length ℓ moving with velocity v through a magnetic field B.

Example:
If B=2 T, ℓ=0.5 m, v=3 m/s, and θ=90∘:
ε=2×0.5×3=3 V
5. Lenz's Law

Formula:
ε=−dϕdt

Explanation:
The induced EMF opposes the change in magnetic flux that caused it.
6. Self-Inductance (L)

Formula:
L=NϕI

Explanation:
Self-inductance (L) is the ratio of the magnetic flux (ϕ) linked with the coil to the current (I) producing it.
7. Induced EMF due to Self-Inductance

Formula:
ε=−LdIdt

Explanation:
The EMF induced due to a changing current in the same coil.
8. Energy Stored in an Inductor

Formula:
U=12LI2

Explanation:
The energy stored in an inductor due to the current I flowing through it.
9. Mutual Inductance (M)

Formula:
M=N2ϕ21I1

Explanation:
Mutual inductance (M) is the ratio of the magnetic flux linked with the second coil to the current in the first coil.
10. Induced EMF due to Mutual Inductance

Formula:
ε2=−MdI1dt

Explanation:
The EMF induced in one coil due to a changing current in another coil.
11. Angular Frequency (ω)

Formula:
ω=2πf

Explanation:
Angular frequency ω is related to frequency f.
12. Power in AC Circuit

Formula:
P=VIcos⁡ϕ

Explanation:
Power (P) in an AC circuit depends on voltage (V), current (I), and phase angle (ϕ).
13. Impedance in Series R-L Circuit

Formula:
Z=R2+(ωL)2

Explanation:
Impedance (Z) of a series circuit with resistance (R) and inductance (L).
14. Resonant Frequency

Formula:
f0=12πLC

Explanation:
The frequency at which a circuit naturally oscillates.

All Important Formula — Class 11 Physics Notes

Topics covered in All Important Formula

1.Optics

1. Snell's Law for Refractive Index

Example:

2. Brewster's Law

Example:

3. Relation Between Refractive Indices

Example:

4. Refractive Index Formula

Example:

5. Mirror Formula

Example:

6. Lens Maker Formula

Example:

7. Equivalent Focal Length for Two Focal Lengths f1 and f2

Example:

8. Power of a Lens

Example:

9. Refraction Through Prism

Example:

2.Oscillation Formulas

1. Differential Equation for SHM

Explanation:

Example:

2. Velocity in SHM

Explanation:

Example:

3. Maximum Velocity (Vmax)

Explanation:

Example:

4. Acceleration in SHM

Explanation:

Example:

5. Displacement in SHM

Explanation:

Example:

6. Time Period for SHM

Explanation:

Example:

7. Angular Frequency (ω)

Example:

8. Potential Energy (P.E.)

Example:

9. Kinetic Energy (K.E.)

Example:

10. Total Energy (T.E.)

Example:

11. Time Period of a Simple Pendulum

Example:

12. Time Period for a Mass-Spring System

Example:

13. Frequency (f)

Example:

3.Gravitation Formulas and Constant Values of Physical Quantities

Gravitation Formulas

1. Newton’s Law of Gravitation

2. Gravitational Constant

3. Acceleration Due to Gravity (g)

4. Gravitational Potential Energy

5. Orbital Velocity (v0)

6. Escape Velocity (ve)

7. Time Period of a Satellite (T)

8. Kepler’s Third Law

9. Weight on a Planet (W)

Constant Values of Physical Quantities

4.Electromagnetic Induction Formula

1. Faraday's Law of Induction

2. Magnetic Flux

3. Induced EMF in a Loop

4. Induced EMF for a Moving Conductor

5. Lenz's Law

6. Self-Inductance (L)

7. Induced EMF due to Self-Inductance

8. Energy Stored in an Inductor

9. Mutual Inductance (M)

10. Induced EMF due to Mutual Inductance

11. Angular Frequency (ω)

12. Power in AC Circuit

13. Impedance in Series R-L Circuit