The box of a pin hole camera of length L, has a hole of radius a. It is assumed that when the hole is illuminated by a parallel beam of light of wavelength `lambda`, the spread of the spot (obtained on the opposite wall of camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would have its minimum size (say `b_(min)`) when.

The box of a pin hole camera, of length L, has a hole of radius a . It is assumed that when the hole is illuminated by a parallel beam of light of wavelength lamda the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size (say b_(min)) when:

The box of a pin hole camera, of length L, has a hole of radius a . It is assumed that when the hole is illuminated by a parallel beam of light of wavelength lamda the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size (say b_(min)) when:

The box of a pin hole camera of length L has a hole of radius a. It is assumed that when the hole is illuminated by a parallel beam of light of wavelength lambda the speed of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size (say b_("min")) when .....

Name the process associated with the following (a) Dry ice is kept at room temperature and at one atmospheric pressure. (b) A drop of ink placed on the surface of water contained in a glass spreads throughout the water. (c) A potassium permanganate crystal is in a beaker and water is poured into the beaker with stirring. (d) An acetone bottle is left open and the bottle becomes empty. (e) Milk is churned to separate cream from it. (f) Settling of sand when a mixture of sand and water is left undisturbed for some time. (g) Fine beam of light entering through a small hole in a dark room. Illuminates the particles in its paths.

There is a fixed sphere of radius R having positive charge Q uniformly spread in its volume. A small particle having mass m and negative charge (– q) moves with speed V when it is far away from the sphere. The impact parameter (i.e., distance between the centre of the sphere and line of initial velocity of the particle) is b. As the particle passes by the sphere, its path gets deflected due to electrostatics interaction with the sphere. (a) Assuming that the charge on the particle does not cause any effect on distribution of charge on the sphere, calculate the minimum impact parameter b0 that allows the particle to miss the sphere. Write the value of b_(0) in term of R for the case 1/2mV^(2)=100.((kQq)/(R)) (b) Now assume that the positively charged sphere moves with speed V through a space which is filled with small particles of mass m and charge – q. The small particles are at rest and their number density is n [i.e., number of particles per unit volume of space is n]. The particles hit the sphere and stick to it. Calculate the rate at which the sphere starts losing its positive charge (dQ)/(dt). Express your answer in terms of b_(0)

The refractive index of light in glass varies with its wavelength according to equation mu (lambda) = a+ (b)/(lambda^(2)) where a and b are positive constants. A nearly monochromatic parallel beam of light is incident on a thin convex lens as shown. The wavelength of incident light is lambda_(0) +-Delta lambda where Delta lambda lt lt lambda_(0) . The light gets focused on the principal axis of the lens over a region AB. If the focal length of the lens for a light of wavelength lambda_(0) is f_(0) , find the spread AB.