(a) (i) What are the two main considerations for designing the objective and eyepiece lenses of an astronomical telescope ? Obtain the expression for magnifying power of the telescope when the final image is formed at infinity. (ii) A ray of light is incident at an angle of $45^\circ$ at one face of an equilateral triangular prism and passes symmetrically through the prism. Calculate : (1) the angle of deviation produced by the prism (2) the refractive index of the material of the prism OR (b) (i) Describe a simple activity to observe diffraction pattern due to a single slit. (ii) The figure below shows an equiconvex lens (of refractive index $1.50$) in contact with a liquid layer on top of a plane mirror. A small needle with its tip on the principal axis is moved along the axis until its inverted image is found at the position of the needle. The distance of the needle from the lens is measured to be $45.0\text{ cm}$. When the liquid is removed and the experiment is repeated, the new distance is $30.0\text{ cm}$. Find the refractive index of the liquid.