Q9.31Multiple choice
An infinitely long cylinder of radius R is made of an unusual exotic material with refractive index –1 (Fig. 9.7). The cylinder is placed between two planes whose normals are along the y direction. The center of the cylinder O lies along the y-axis. A narrow laser beam o R is directed along the y direction from the lower plate. The laser r source is at a horizontal distance x from the diameter in the y direction. Find the range of x such that light emitted from the i lower plane does not reach the upper plane. Fig. 9.7 9.32
This question refers to a figure in the original PDF.
- (i)Consider a thin lens placed between a source (S) and an observer (O) (Fig. 9.8). Let the thickness of the lens vary as b2 w(b ) = w0 – , where b is the verticle distance from the pole. α w0 is a constant. Using Fermat’s principle i.e. the time of transit Ray Optics and Optical Instruments for a ray between the source and observer is an P1 extremum, find the condition that all paraxial rays starting from the source will converge at a point O S u v O on the axis. Find the focal length.
- (ii)A gravitational lens may be assumed to have a varying Fig. 9.8 width of the form k w(b ) = k1ln 2 bmin < b < bmax b k = k1ln 2 b < bmin bmin Show that an observer will see an image of a point object as a ring about the center of the lens with an angular radius ( n – 1) k1 β= v . u +v