Physics - Geometrical Optics Question with Solution | TestHub
It should be possible to make a lens from some inhomogeneous material, one where there is a GRadient in the INdex of refraction; such a device is known as GRIN lens. A powerful incentive for developing such systems is that they provide the optical designer with an additional set of new parameters with which to control aberrations.
To get a rough sense of how a GRIN lens might work, consider the device pictured in figure (a) and (b) where, for simplicity, we assume f > r. This is a flat disk of glass that has been treated so that it has an index n(r) that drops off radially in some as yet undetermined fashion from a maximum value of nmax on the optical axis. Accordingly, it's called a radial-GRIN device. A ray that traverses the disk on the optical axis passes along an optical path length of (OPL)O = nmax*d, whereas for a ray traversing at height r, overlooking the slight bending of its path, (OPL)r ≈ n(r)*d. Since a planar wavefront must bend into a spherical wavefront, the OPLs from one to the other, along any route must be equal: (OPL)r + AB = (OPL)O, so n(r) = nmax - AB/d. But AF ≈ √(r² + f²); moreover, AB = AF - f. Rewriting the square root via the Binomial theorem, n(r) becomes:
This tells us that if the index of refraction drop off parabolically from its height along the central axis, the GRIN plate will focus a collimated beam at F and serve as a positive lens. Although this is a rather simplistic treatment, it does make the point: a parabolic refractive index profile will focus parallel light.
Today a variety of radial-GRIN lenses are commercially available and tens of millions of them are already in service in laser printers, photocopiers, and fax machines.
An alternative approach to the flat-faced radial-GRIN rod is the axial-GRIN lens which is generally polished with spherical surfaces. Every annulus (concentric with the optical axis) on the lens's face has a gradually changing index. Rays impinging at different heights above the optical axis encounter glass with different indices and bend appropriately. On the contrary, a normal lens shows spherical aberration. The spherical aberration evident in figure (d) arises because the edges of the spherical lens refract too strongly. Gradually lowering the index of refraction out toward the edges allows the axial-GRIN lens to correct for spherical aberration.
Figure (a):
Figure (b):
Figure (c):
Figure (d):
. The paragraph suggests that in plano convex axial GRIN lens
Options:
Answer:
Solution:
In the plano-convex axial GRIN lens, focusing is achieved by a refractive index that is maximum on the axis and falls off away from it, so that off-axis rays travel faster and all rays arrive together. Hence (D): refractive index decreases with distance from the z-axis.
