(i) Similar to a rectangular slit, when a circular aperture or opening (like a lens or the iris of our eye) forms an image of a point object, the image formed will not be a point but a diffraction pattern of concentric circles that become fainter while moving away from the center as shown in Figure. These are known as Airy's discs
\(asin\theta =1.22\lambda \) 

(ii) Here, the numerical value 1.22 comes for central "maximum formed by circular apertures.
For small angles, sin θ = θ
\(a\theta =1.22\lambda \) 
Rewriting further,
\(\theta =\cfrac { 1.22\lambda }{ a } \ and \cfrac { { r }_{ o } }{ f } =\cfrac { 1.22\lambda }{ a } \)
\({ r }_{ o }=\cfrac { 1.22\lambda f }{ a } \)

(i) The line joining the pole and the centre of curyature is called the principal axis of the mirror.
(ii) The light ray travelling along the principal axis towards the mirror after reflection travels back along the same principal axis. It is also called optical axis.

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.

There are two ways of preparing the nanomateials, top down and bottom up approaches

Rate of disintegration of a radioactive sample,
R = \(\frac{dN}{dt}\)
According to radioactive decay law
- \(\frac{dN}{dt}\) ∝ N
- \(\frac{dN}{dt}\) = λN or R = λN

It is produced by Sun, arc, and ionized gases. The wavelength range is 6 x 10^-10m to 4 x 10^-7m and the frequency range is 5 x 10¹⁷Hz to 7 x 10¹⁴Hz. It has less penetrating power. It can be absorbed by atmospheric ozone and harmful to human body. It is used to destroy bacteria, sterilizing the surgical instruments, burglar alarm, detect the invisible writing, finger prints and also in the study of molecular structure.

(i) Magnets are classified into natural magnets and artificial magnets.
(ii) For example, iron, cobalt, nickel, etc. are natural magnets.
(iii) Strengths of natural magnets are very weak and the shapes of the magnet are irregular.
(iv) Artificial magnets are made by us in order to have desired shape and strength.
(v) If the magnet is in the form of rectangular shape or cylindrical shape, then it is known as bar magnet.

Current lags behind the applied voltage  \(\frac{\pi}{2}\) in an inductive circuit. This fact is depicted in the phasor diagram. In the wave diagram also, it is seen that current lags the voltage by 90°.

(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) 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.