both its surfaces polished intospherical surfaces. The front surface is convex a

Question

  both its surfaces polished intospherical surfaces. The front

  surface is convex and has a radius ofcurvature IR1I=5.00cm,

   while the back surface is concaveand has a radius of curvature

   IR2I=6.00cm. Refer tothe figure to the right. The disk is in air and

   acts like a thick lens. A brightobject of height h=2.00 cm is

   located on the optic axis 5.00 cm tothe left from vertex V1. The

   final image is virtual and it is seen6.00 cm behind vertex V2, with

   an eye positioned close to the opticaxis.

(a)   Find the thickness d of the lens,i.e., the distance between vertices V1 andV2.

Explanation / Answer

(a)according to thin flim interference 2nd * cos1 = m * ----------(1) applying Snell's law to the air glass interface n * sin1 = n' * sin or 1 = sin-1(n' * sin/n)-----------(2) from (1) d = (m * /2n * cos1) here,m = 1 is the wavelength of light used n = 1 (refractive index of air) the value of 1 is obtained from equation (2) the wavelength is = (2/k) where k is the wavenumber and is equal to 5.00 cm or = (2/5.00 * 10^-2) = 125.6 m (b)the magnification is m = (v/u) v = 6.00 cm and u = 5.00 cm or m = (6.00/5.00) = 1.2 or m = (I/O) or I = m * O = 1.2 * 2.00 = 2.4 cm the height of the final image is I = 2.4 cm the image formed by the lens is behind vertexV2.Point P' is a virtual image of the object pointP.Furthermore,it is an uright image,having the same orientation asthe object.The refracted rays,which are all to the right of thelens,appear on a screen placed in the image plane at P'.

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