The equation of refraction at a spherical surface is `mu_2/v-mu_1/u=(mu_2-mu_1)/R`
Taking `R=oo`, show that this equation leads to the equation
`(Real depth)/(Apparent depth)=mu_1/mu_2` for fraction at a plane surface.

A curved surface of radius R separates two medium of refractive indices mu_(1) "and" mu_(2) as shown in figures A and B . Identity the correct statement(s) related to the formation of images of a real object O placed at x from the pole of the concave surface, as shown in figure B

A point source S is placed at the bottom of different layers as shown is figure,the refractive index of bottommost layer is mu_(0) The refractive index of any other upper layer is mu(n)=mu_(0)-(mu_(0))/(4pi-18) where n=1,2,..... A ray of light starts form the source S as shown. Total internal reflection takes place at the upper surface of a layer haing n equal to

Give equation which relate c,mu_(0),in_(0) .

There is a spherical glass ball of refractive index mu_(1) and another glass ball of refractive index mu_(2) inside as shown in figure . The radius of the outer ball is R_(1) and that of inner ball is R_(2) . A ray is incident on outer surface of the ball at an angle i_(1) , Find the value of r_(2)

There is a spherical glass ball of refractive index mu_(1) and another glass ball of refractive index mu_(2) inside as shown in figure . The radius of the outer ball is R_(1) and that of inner ball is R_(2) . A ray is incident on outer surface of the ball at an angle i_(1) , Find the value of r_(1)

There is a spherical glass ball of refractive index mu_(1) and another glass ball of refractive index mu_(2) inside as shown in figure . The radius of the outer ball is R_(1) and that of inner ball is R_(2) . A ray is incident on outer surface of the ball at an angle i_(1) , Find the value of i_(2)

The adjacent figure shows a thin plano-convex lens of refractive index mu_1 and a thin plano-concave lens of refractive index mu_2 , both having same radius of curvature R of their curved surfaces. The thin lens of refractive index mu_3 has radius of curvature R of both its surfaces. This lens is so placed in between the plano-convex and plano-concave lenses that the plane surfaces are parallel to each other. The focal length of the combination is

A curved surface of radius R separates two medium of refractive indices mu_(1) "and" mu_(2) as shown in figures A and B . Choose the correct statement(s) related to the real image formed by the object O placed at a distance x, as shown in figure A.

A rectangulat block of refractive index mu is placed on a printed page lying on a horizontal surface as shown in Fig. , Find the minimum value of mu so that the letter L on the page is not visible from any of the vertical sides.

The optical properties of a medium are governed by the relative permitivity (epsi_(r)) and relative permeability (mu_(r)) . The refractive index is defined as sqrt(mu_(r)epsi_(r))=n . For ordinary material epsi_(r)gt0 and mu_(r)gt0 and the positive sign is taken for the square root. In 1964, a Russian scientist V. Veselago postulated the existence of material with epsi_(r)lt0andmu_(r)lt0 . Since then such 'metamaterials' have been produced in the laboratories and their optical properties studied. For such materials n=-sqrt(mu_(r)epsi_(r)) . As light enters a medium of such refractive index the phases travel away from the direction of propagation. (i) According to the description above show that if rays of light enter such a medium from air (refractive index = 1) at an angle theta in 2^(nd) quadrant, then the refracted beam is in the 3^(rd) quadrant. (ii) Prove that Snell's law holds for such a medium.