Explain the terms interference of light and define constructive and destructive interference. Is law of conservation of energy obeyed?

Distinguish between interference and diffraction.

The mixture a pure liquid and a solution in a long vertical column (i.e., horizontal dimensions << vertical dimensions) produces diffusion of solute particles and hence a refractive index gradient along the vertical dimension. A ray of light entering the column at right angles to the vertical deviates from its original path. find the deviation in travelling a horizontal distance d<

(i) Consider a thin lens placed between a source (S) and an observer (O). Let the thickness of the lens vary as \(\omega (b)={ \omega }_{ 0 }-\frac { { b }^{ 2 } }{ a } ,\) where b is the vertical distance from the pole. \({ \omega }_{ 0 }\) is a constant. using Fermat's principle i.e., the time of transit for a ray between the source and observer is an extremum, find the condition that all paraxial rays starting from the source will converge at a point O on the axis. find the focal length

(ii) A gravitational lens may be assumed to have a varying width of the form show that an observer will see an image of a point object as a ring about the centre of the lens with an angular radius \(\beta =\sqrt { \frac { (n-1){ k }_{ 1 }\frac { u }{ v } }{ u+v } } \) 

A refracting telescope has an objective of focal length 1m and an eye of the sun 10 cm in diameter is formed at a distance of 24cm from eye piece. What angle does the sun subtend at the objective?

Use the mirror equation to deduce that, The virtual image produced by a convax mirror is always diminished in size and is located between the focus and the pole.

How is the working of telescope different from that of a microscope?
The focal lengths of the objective and eyepiece o a microscope are 1.25 cm and 5 cm, respectively. Find the position of the object relative to the objective in order to obtain an angular magnification of 30 in normal adjustment.

Ravi wanted to buy a gift for his sister and so he entered inside a gift shop. The gift shop had many glass items. On looking closely, he found many of the beverage glasses used for cold drinks had big thick glass walls. He decided not to buy these glasses because he knows that this gives a false impression that there is more amount of liquid inside the glass.
Read the above passage and answer the following questions:
(i) How does Ravi know about the false impression given by the beverage glasses made with very thick glass walls?
(ii) What values can you associate with Ravi decision?

A child is observing a thin film such as a layer of oil on water showing beautiful colours, when illuminated by white light. He feels happy and surprised to see this.His teacher explains him example of spreading of kerosene oil on water to prevent malaria and dengue.
Read the above passage and answer the following questions:
(i) What values are displayed by his teacher?
(ii) Name the phenomenon involved.

(i) How does one demonstrate, using a suitable diagram, that unpolarised light when passed through a polaroid gets polarised?
(ii) A beam of unpolarised light is incident on a glass-air interface. Show, using a suitable ray diagram, that light reflected from the interface is totally polarised, when \(\mu =tan{ i }_{ B }\) where \(\mu \) is the refractive index of glass with respect to air and \({ i }_{ B }\) is the Brewster's angle.