OPTICS

1. 
   where f  is the focal length,
   u  is the distance between the object and the back of the mirror,
   and       v  is the distance between the image and the back of the mirror.
2. 
   where m is the magnification,
   u is the distance between the object and the back of the mirror,
   and       v is the distance between the image and the back of the mirror.
   
   NOTE:             For a concave mirror and a converging lens .
                           For a convex mirror and a diverging lens .
   
                           For a real image .
                           For a virtual image .
3. Snell’s Law:
   
   where   i is the angle of incidence, r is the angle of refraction and n is the refractive index.
4. 
5. 
   where c is the critical angle and n is the refractive index.
6. 
   where  is the speed of light in a vacuum,  is the speed of light in glass and n is the refractive index.
7. 
   where  is the speed of light in medium 1,  is the speed of light in medium 2
   and  is the refractive index between the two media.
8. 
   where P is the power of a lens and f is its the focal length.
   (Remember to express f in metres.)
9. 
   where P is the power of a pair of lenses in contact,  is the power of the first lens and  is the power of the second lens.
10. 
    where f is the focal length of a pair of lenses in contact, is the focal length of the first lens and  is the focal length of the second lens.

MECHANICS

1. Galilean Equations of Motion under Constant Acceleration
                       (No s)
                  (No v)
                 (No t)
   
   where   a = constant acceleration
   u = initial velocity
   v = final velocity
   s = displacement
   and       t = time taken.
   
   Note: For a projectile at maximum height the speed is zero.
2. 
   where p is momentum, m is mass and v is velocity.
3. Conservation of Momentum
   
   where a pair of masses  and  have velocities  and  respectively.
   After they interact they have velocities  and  respectively.
4. or
   where F is force, p is momentum and t is time
   or         F is average force, m is mass, v is final velocity and u is initial velocity.
5. Newton’s Second Law.
   
   where F is force, m is mass and a is acceleration.
6. 
   where W is the weight of an object of mass m and g is the acceleration due to gravity.
7. and
   where x is the horizontal component and y is the vertical component of a vector v which is at angle of  to the horizontal.

8. 
   where P is pressure, F is force and A is area.

9. 
   where  is the density of a body with mass m and volume V.
10. 
    where P is the pressure in a fluid,  is the density of the fluid, g is the acceleration due to gravity and h is the depth at which the pressure is being taken.
11. Boyle’s Law
    
    where P is the pressure of an ideal gas and V is its volume.
12. 
    where F is the gravitational force between a mass  and a mass  separated by a distance of d metres and where G is the universal gravitational constant.
13. 
    where g is the acceleration due to gravity at a distance d from a planet of mass M.
    G is the universal gravitational constant.
14. 
    where M is the moment of a force F applied at a distance d from a given point.
15. 
    where T is the torque (moment) of a couple, i.e. a pair of force each of magnitude F, having opposing directions and separated by a distance d.
16. 
    where W is the work done when a force F moves a body a distance s in the direction of the force.
17. 
    where  is the kinetic energy of a body of mass m and velocity v.
18. 
    where  is the potential energy required to move a mass m a vertical distance h and g is the acceleration due to gravity.
19. 
    where P is the average power when W is the work done in a time t.
20. 
21. 
    where  is the angle in radians corresponding to an arc length l in a circle of radius length r.
22. 
    where  is the average angular speed when a body in circular motion traces an angle of  radians in t seconds.
23. 
    where v is the tangential velocity of an object moving in a circle of radius length r with a constant angular speed .
24.            or        
    where a is the centripetal acceleration of a body moving in a circle of radius length r with a constant angular velocity  and a tangential velocity v.
25. or
    where F is the centripetal force required to keep a body of mass m moving in a circle of radius r. The body moves with a constant angular velocity  and a tangential velocity v.
26. 
    where v is the speed of a satellite in a circular orbit of radius R around a planet of mass M. G is the universal constant of gravitation.
27. 
    where T is the period of a satellite moving at a constant velocity v in a circular orbit of radius R.
28. Kepler’s Third Law
    
    where T is the period of a a circular orbit of radius R around a planet of mass M.  G is the universal constant of gravitation.
29. 
    where R is the radius of a circular orbit of period T around a planet of mass M.  G is the universal constant of gravitation.
    
    Note: for a geostationary or parking orbit T = one day = 86, 400 seconds. The height, h, of such an orbit is given by , where r is the radius of the planet..
30. Hooke’s Law
    
    where F is the force required to give a spring a displacement s and k is a constant of proportionality. (Note: the spring must not be extended by beyond its elastic limit.)
31. 
    where a is the acceleration of a body moving in simple harmonic motion when it has a displacement s from its equilibrium position. The constant of proportionality is given by .
32. 
    where T is the period of a body moving in simple harmonic motion with a constant of proportionality .
33. 
    where T is the period of a simple pendulum of length l and g is the acceleration due to gravity.

TEMPERATURE AND HEAT

1. 
   where t is the temperature in degrees Celsius and T is the temperature in Kelvin.
2. 
   where Q is the heat required / liberated when a body is of heat capacity C changes its temperature by  degrees Celsius without changing its state.
3. 
   where Q is the heat required / liberated when a mass m of specific heat capacity c changes its temperature by  degrees Celsius.
4. To find the specific heat of water by the electrical method:
   
   Heat delivered by electrical coil = heat gained by water + heat gained by calorimeter
   
5. 
   where Q is the heat required / liberated when a mass m of specific latent heat l changes its state without changing its temperature.
6. To find the specific latent heat of fusion of ice:
   
   Heat gained by ice in melting and then heating = heat lost by warm water + heat lost by calorimeter
   
   
7. To find the specific latent heat of vaporisation of water:
   
   Heat lost by steam in condensing and then cooling = heat gained by water + heat gained by calorimeter
   
   
8. 
   where U is the U-value of a structure when heat energy Q is conducted in t seconds through an area A with a temperature difference of  between its ends.

WAVES

1. 
   where c is the speed of a wave, f is its frequency and  is its wavelength.
2. 
   where f’ is the observed frequency, f is the actual frequency, c is the speed of the wave and v is the speed of the source.
   (Note: Take minus for approaching waves and plus for receding waves.)
3. 
   where I is sound intensity, P is power and A is an area at right angles to the direction of the sound at that point.
4. 
   where f is the fundamental frequency, l the length, T the tension and  the mass per unit length of a stretched string.
5. To measure the speed of air using a resonance tube:
   
6. or
   where d is the distance between two adjacent slits, i.e. the grating constant, of a diffraction grating with n lines per millimetre.
7. To measure the wavelength of light with a diffraction grating:
   
   where n is the order of the image,  is the wavelength of the light, d is the grating constant and  is the angle between the n^th  image and the central image.

STATIC ELECTRICITY

1. 
   where F is the force between two charges Q₁ and Q₂ a distance d apart in a medium of permittivity .

2. 
   The permittivity of a medium is given by its relative permittivity times the permittivity of a vacuum.
3. 
   If a charge Q experience a force F when placed in an electric field, then the field strength is given by E.
4. 
   where W is the energy gained when a charge Q is accelerated by a potential difference V.
5. 
   where C is the capacitance of a conductor which has a charge Q and a potential V.
6. 
   where C is the capacitance of a parallel plate capacitor. The common area of the plates is A. The distance between the plates is d. The permittivity of the medium between the plates is .
7. 
   where W is the energy stored in a capacitor of capacitance C with a potential V.

CURRENT ELECTRICITY

1. 
   where P is the power dissipated when a current I is driven by a potential difference V.
2. The definition of resistance:
   
   where R is the resistance of a material when a potential difference V across it drives a current I.
3. Ohm’s Law:
   A conductor obeys Ohm’s law if the potential difference, V, across its ends is directly proportional to the current, I, flowing through it whenever the temperature is constant, i.e.
   
4. 
   where R is the effective resistance of three resistors in series.
5. 
   where R is the effective resistance of three resistors in parallel.
6. 
   where  is the resistivity of a conductor of uniform cross section A, length l and resistance R.
7. 
   where  is the resistivity of a wire of diameter d, length l and resistance R.
8. Wheatstone Bridge Formula (when the bridge is balanced):
   

9. Joule’s Law:
   
   the heat, W, liberated when a current I flows through a wire of resistance R for a time t.
10. 
    where P is the power developed in a wire of resistance R when it carries a current I.

MAGNETISM and INDUCTION

1. 
   where F is the force experienced by a conductor carrying a current I in a field of magnetic flux density B.
2. 
   where F is the force experience by a charge q moving with velocity v in a field of magnetic flux density B.
3. 
   used to find the radius, r, of the circular orbit of a charge q, mass m, moving with velocity v in a B-field.
4. 
   where  is the magnetic flux threading an area A at right angles to a field of magnetic flux density B.
5. Faraday’s Law of Electromagnetic Induction
   
   where E is the average induced e.m.f.,  and  the initial and final magnetic flux respectively, and t is the time taken for the change in magnetic flux.
   (Note: if a coil has N turns, then this value has to be multiplied by N to get the total induced e.m.f.)
6. Faraday’s Law of Electromagnetic Induction
   
7. 
   relates the r.m.s. and peak values of a.c.
8. 
   relates the r.m.s. and peak values of an a.c. voltage.
9. 
   the power, P, developed by an a.c. is equal to the product of the r.m.s. values of potential difference and of current.
10. 
    the power developed by an a.c. is equal to the square of the r.m.s. value of the current multiplied by the resistance through which it flows.
11. 
    The ratio of the voltage across the primary to the voltage across the secondary coil of a transformer is equal to the ratio of the number of turns in the primary to the number of turns in the secondary.
    (Note: But )

THE ELECTRON

1. 
   the kinetic energy gained by an electron in accelerating through a potential difference V.
2. 
3. 
   where E is the energy of a photon, h is Planck’s constant and f is the frequency of the photon.
4. 
   where E is the energy of a photon, h is Planck’s constant and  is the wavelength of the photon.
5. 
   where  is the work function (the minimum energy required to just free an electron from a metal), h is Planck’s constant and  is the minimum frequency of light which will liberate an electron from a metal.
6. 
   where hf is the energy of an incident photon,  is the work function of a metal and  is the maximum kinetic energy of the resulting photo-electron.

THE ATOM

1. Law of Radioactive Decay
   
   where  is the activity, or rate of decay,  is the decay constant and N the number of undecayed nuclei.
2. 
   where  is the half-life of a radioactive isotope and  is the decay constant.
3. Avogadro’s Number
   
   Note: the mass of any element expressed in grams, e.g. 12g of carbon, contains this number of atoms.
4. 
   where E is the energy lost / gained when there is a mass excess / deficit m in a reaction and c is the speed of light in vacuo.
5. Pair Production
   
6. Pair Annihilation