\(\cfrac { 1 }{ v } -\cfrac { 1 }{ u } =\cfrac { 1 }{ f } \) or \(\cfrac { 1 }{ v } =\cfrac { 1 }{ f } +\cfrac { 1 }{ u } \) 
convex lens : f > 0 ; u < 0 (object on the left)
For 0 < I u I \(\cfrac { 1 }{ v } =\cfrac { 1 }{ f } -\cfrac { 1 }{ |u| } <0\) i.e. u < 0 (image on left; virtual)
Also for this case, \(\cfrac { 1 }{ \left| v \right| } <\cfrac { 1 }{ |u| } .i.e.\left| u \right| <\left| v \right| \) (image enlarged)

Work function W = hv_o = \(\frac{hc}{\lambda_o}\)
\({ \lambda }_{ o }\alpha \frac { 1 }{ W } \)
As W_AB; (\({ \lambda }_{ o }\)) _A > (\({ \lambda }_{ o }\)) _B
i.e., the threshold wavelength of metal A is higher.

Laws of photoelectric effect:
(i) For a given surface, the emission of photoelectrons takes place only if the frequency of incident light is greater than a certain minimum frequency called the threshold frequency.
(ii) For a given frequency of incident light, the number of photoelectrons emitted is directly proportional to the intensity of the incident light. The saturation current is also directly proportional to the intensity of incident light.
(iii) Maximum kinetic energy of the photoelectrons is independent of the intensity of the incident light.
(iv) Maximum kinetic energy of the photoelectrons from a given metal is directly proportional to the frequency of incident light.
(v) There is no time lag between the incidence of light and the ejection of photoelectrons.

(i) Face recognition.
(ii) Providing response to player's actions in computer games.
(iii) Taking decisions based on previous actions.
(iv) To regulate the traffic by analyzing the density of traffic on roads.
(v) Translate words from one language to another.

i) The TV signals are frequency modulated. The transmission of TV signals cannot be obtained the ground wave propagation, as such signals get absorbed by ground due to their high frequency.
ii) TV signals cannot be transmitted via skywave propagation as the ionosphere is unable to reflect radio waves of frequencies greater than 40 MHz.
iii) Therefore, the only way out for the transmission of TV signals is that receiving antenna should directly intercept the signal from the transmitting antenna.

Advantages of AM :
(i) Easy transmission and reception
(ii) Lesser bandwidth requirements
(iii) Low cost
Limitations of AM :
i) Noise level is high
i) Low efficiency
ii) Small operating range

(i) Energy-produced per fusion is less but the number of nuclei per unit mass is larger on account of smaller mass number.
(ii) So, energy released per unit mass is greater. On the other hand, the fissionable materials have high atomic weight.
(iii) The number of fission nuclei per unit mass is less. So, energy released is less.

The neutrino has the following properties
(i) It has zero charge
(ii) It has an antiparticle called anti-neutrino.
(iii) Recent experiments showed that the neutrino has very tiny mass
(iv) It interacts very weakly with the matter. Therefore, it is very difficult to detect In fact, in every second, trillions of neutrinos coming from the sun are passing through our body without any interaction.

(i) u - v rays
(ii) X - rays
(iii) ૪ - rays.

(i) It is produced by transitions of atomic nuclei and decay of certain elementary particles. They produce chemical reactions on photographic plates, fluorescence, ionization, diffraction.
(ii) Gamma rays provide information about the structure of atomic nuclei. It is used in radiotherapy for the treatment of cancer and tumor, in the food industry to kill pathogenic microorganisms.

A galvanometer cannot be used for measuring the current
(i) A galvanometer has a finite large resistance and is connected in series in the circuit. So it will increase the resistance of circuit and hence change the value of current in the circuit.
(ii) A galvanometer is a very sensitive device, it gives a full scale deflection for the current of the order of microampere hence if connected, it will not measure current of the order of ampere.

Net force an electron moving in the combined electric field \(\vec { E } \) and a magnetic field \(\vec { B } \) is
\(\vec { F } =-e[\vec { E } +\vec { v } \times \vec { B } ]\)
Since electron moves undeflected then \(\vec { F } \) = 0
\(\vec { E } +(\vec { v } \times \vec { B } )\) = 0
\(|\vec { E } |=(|\vec { v } |\times |\vec { B } |)\Rightarrow |\vec { v } |=\frac { |\vec { E } | }{ |\vec { B } | } \). 

(i) Magnetic field lines are continuous closed curves. The direction of magnetic field lines is from the North pole to the South pole outside the magnet and South pole to the North pole inside the magnet.
(ii) The direction of a magnetic field at any point on the curve is known by drawing a tangent to the magnetic line of force at that point.
(iii) Magnetic field lines never intersect each other.
(iv) The degree of closeness of the field lines determines the relative strength of the magnetic field. The magnetic field is strong where magnetic field lines crowd and weak where magnetic field lines thin out.

(i) The total resistance offered to the flow of current due to resistance R, inductive resistance X_L, and capacitive reactance X_c in a circuit is called impedance.
It is given by \(z=\sqrt { { R }^{ 2 }+({ { X }_{ L }-{ X }_{ C }) }^{ 2 } } \)
(ii) At resonance, when X_L= X_C

(i) Suppose n cells, each of emf \(\xi \) volts and internal resistance r ohms are connected in series with an external resistance R.
(ii) The total emf of the battery = \(n\xi \) The total resistance in the circuit = nr + R By Ohm's law, the current in the circuit is 
\(I=\cfrac { totalemf }{ taoal\ resistance } =\cfrac { n\xi }{ nr+R } \)
\(I=\cfrac { n\xi }{ R } =n{ l }_{ 1 }\)
(iii) where II is the current due to a single cell
\(\left( { I }_{ 1 }=\cfrac { \xi }{ R } \right) \)
Thus, if r is negligible when compared to R the current supplied by the battery is n times that supplied by a single cell.
Case (b) If r >> R,\(I=\cfrac { n\xi }{ nr } =\cfrac { \xi }{ r } \)
(iv) It is the current due to a single cell. That is, current due to the whole battery is the same as that due to a single cell and hence there is no advantage in connecting several cells.
(v) Thus series connection of cells is advantageous only when the effective internal resistance of the cells is negligibly small compared with R.

Phasor: A sinusoidal alternating voltage (or current) can be represented by a vector that rotates about the origin in an anti-clockwise direction at a constant angular velocity ω. Such a rotating vector is called a phasor. A phasor is drawn in such a way that
(i) the length of the line segment equals the peak value Vm (or I_m) of the alternating voltage (or current)
(ii) its angular velocity w is equal to the angular frequency of the alternating voltage (or current)
(iii) the projection of phasor on any vertical axis gives the instantaneous value of the alternating voltage (or current)
(iv) the angle between the phasor and the axis of reference (positive x-axis) indicates the phase of the alternating voltage (or current).
The notion of phasors is introduced to analyze the phase relationship between voltage and current in different AC circuits.
Phasor diagram
The diagram which shows various phasors and their phase relations is called the phasor diagram.

(i) For conductors a is positive. If the temperature of a conductor increases, the average kinetic energy of electrons in the conductor increases. This results in more frequent collisions and hence the resistivity increases.
(ii) The graph of the Even though, the resistivity of conductors like metals varies linearly for a wide range of temperatures, there also exists a nonlinear region at very low temperatures.
(iii) The resistivity approaches some finite value as the temperature approaches absolute zero.
(iv) As the resistance is directly proportional to the resistivity of the material, we can also write the resistance of a conductor at temperature T °C as
\({ R }_{ T }=R\left[ 1+\alpha \left( T-{ T }_{ 0 } \right) \right] \)
\(\alpha =\cfrac { { R }_{ T }-{ R }_{ 0 } }{ { R }_{ 0 }\left( T-{ T }_{ 0 } \right) } =\cfrac { 1\Delta R }{ { R }_{ 0 }\Delta T } \)
\(\alpha =\cfrac { 1 }{ { R }_{ 0 } } \cfrac { \Delta R }{ \Delta T } \)
where \(\Delta R={ R }_{ 1 }-{ R }_{ 0 }\) is a change in resistance during the changing temperature \(\Delta T=T-{ T }_{ 0 }\)

(i) A dielectric is a non-conducting material and has no free electrons. The electrons in a dielectric are bound within the atoms. Ebonite, glass and mica are some examples of dielectrics.
(ii) When an external electric field is applied, the electrons are not free to move anywhere but they are realigned in a specific way. A dielectric is made up of either polar molecules or non-polar molecules.

If the electric field is not uniform, then the force experienced by +q is different from that experienced by -q. In addition to the torque, there will be net force acting on the dipole.