(i) Its cost is very high due to scarity of large and flawless calcite crystals
(ii) Due to extraordinary ray passing obliquely through it the emergent ray is always displaced a little to one side.
(iii) The effective field of view is quite limited
(iv) Light emerging out of it is not uniformly plane polarised.

(i) When light rays incident on a spherical mirror, after reflection, the rays converge at a point on the principal axis for concave mirror or appear to diverse from a point for convex Mirror.
(ii) This point is called the focus or focal point (F) of the mirror.

a) The number of photons incident normally per unit area per unit time is determined by the intensity of radiations.
b) (i) Red light, because the energy of red light is less than that of blue light
(hv)_R < (hv)_B
(ii) Blue light, because the energy of blue light is greater than that of red light
(hv)_B > (hv)_R

(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.

i) Large decrease in noise. This leads to an increase in signal-noise ratio.
ii) The operating range is quite large.
iii) The transmission efficiency is very high as all the transmitted power is useful.
iv) FM bandwidth covers the entire frequency range which humans can hear. Due to this, FM radio has better quality compared to AM radio.

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.

(a) X - rays are used as diagnostic tool in medicine. X-rays are used extensively in studying structures of inner atomic electron shells and crystal structures. It is used in detecting fractures, diseased organs, formation of bones and stones, observing the progress of healing bones. Further, in a finished metal product, it is used to detect faults, cracks, flaws and holes.
(b) Radio are produced by oscillators in electric circuits. It obeys reflection and diffraction. It is used in radio and communication system and cellphones.

(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.

The magnetic field at the center of a circular coil
B = \(\frac { { \mu }_{ 0 }NI }{ 2R } \)
When current I is doubled and radius R is halved,
B' = \(\frac { { \mu }_{ 0 }N\times 2I }{ 2\left( \frac { R }{ 2 } \right) } \)  = 4B
∴ magnetic field becomes four times the original field.

The magnetic field from the center of a circular loop of radius R along the axis is given by
\(\vec { B } =\frac { { \mu }_{ 0 }I }{ 2 } \frac { { R }^{ 2 } }{ ({ R }^{ 2 }+{ z }^{ 2 })^{ \frac { 3 }{ 2 } } } \hat { k } \)
At larger distance z >> R, therefore R² + z² ≈ z²,
we have
\(\vec { B } =\frac { { \mu }_{ 0 }I }{ 2 } \frac { { R }^{ 2 } }{ { z }^{ 3 } } \hat { k } \)               ........(1)
Let A be the area of the circular loop A = πR². So rewriting the equation (1) in terms of the area of the loop, we have
\(\vec { B } =\frac { { \mu }_{ 0 }I }{ 4\pi } \frac { { R }^{ 2 } }{ { z }^{ 3 } } \hat { k } \)
\(\vec { B } =\frac { { \mu }_{ 0 } }{ 4\pi } \frac { 2IA }{ { z }^{ 3 } } \hat { k } \)              .......(2)
Comparing equation (2) with equation (1) dimensionally, we get
p_m = IA
where P_m is called a magnetic dipole moment. In vector notation,
\(\vec { { p }_{ m } } =I\vec { A } \)       .........(3)
This implies that a current - carrying circular loop behaves as a magnetic dipole of the magnetic moment \(\vec { { p }_{ m } } \) So, the magnetic dipole moment of any current loop is equal to the product of the current and area of the loop.

(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) When an electric current is passed through a circuit of a thermocouple, heat is evolved at one junction and absorbed at the other junction. This is known as the Peltier effect.
(ii) In the Cu-Fe thermocouple the junctions A and B are maintained at the same temperature.
(iii) Let a current from a battery flow through the thermocouple. At junction A, where the current flows from Cu to Fe, heat is absorbed and junction A becomes cold.
(iv) At junction B, where the current flows from Fe to Cu heat is liberated and it becomes hot.

Peltier effect: Cu - Fe thermocouple
(v) When the direction of current is reversed, junction A gets heated and junction B gets cooled as shown in Figure (b).
Hence Peltier effect is reversible.

Current lags behind the applied voltage by \(\frac{\pi}{2}\) in an inductive circuit.

(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) This device consists of a long thick copper rod passing from top of the building to the ground. The upper end of the rod has a sharp spike or a sharp needle as shown in Figure 1.64 (a) and (b).
(ii) The lower end of the rod is connected to the copper plate which is buried deep into the ground. When a negatively charged cloud is passing above the building, it induces a positive charge on the spike.
(iii) Since the induced charge density on thin sharp spike is large, it results in a corona discharge.
(iv) This positive charge ionizes the surrounding air which in turn neutralizes the negative charge in the cloud.

(v) The negative charge pushed to the spikes passes through the copper rod and is safely diverted to the earth.
(vi) The lightning arrester does not stop the lightning; rather it diverts the lightning to the ground safely.

(i) Microwave oven works on the principle of torque acting on an electric dipole. The food we consume has water molecules which are permanent electric dipoles.
(ii) Oven produces microwaves that are oscillating electromagnetic fields and produce torque on the water molecules.
(iii) Due to this torque on each water molecule, the molecules rotate very fast and produce thermal energy. Thus, heat generated is used to cook the food.