Question

The Second Edition of the Oxford English Dictionary is currently available as a 20-volume print edition and costs $895. Imagine that the publishers would like to distribute a lower-cost version of the dictionary that still contains all of the same words, but in a smaller number of volumes. To accomplish this, they decide to reduce the font size to 1/3 of the original font size and include a simple biconvex single-lens magnifier with the new reduced-volume set. (a) Fully specify a design for the required single lens magnifier. (b) If the publishers had wanted to severely reduce the font size to 1/15 of the original size, could they still supply a single-lens magnifier for the customers to use? Specify a design for such a magnifier and identify any physical and/or optical performance limitations that arise. What is the maximum diameter possible for this magnifying lens?

Answer 1

(a)

When the font size is reduced to , then we need a magnification of 3 times, in order to bring it to the original font size.

Now, the magnification of a lens is given by the equation

where v is the image distance and u is the object distance from the lens

Now, for a biconvex lens, the object distance is considered -ve, and since we need a virtual image, the image distance will also be -ve.

Now

using lens formula, we get

So we can use any lens, whose focal length is 3/4 times the object distance.

the typical object distance is from about 1 cm to about 16cm, So theoretically, we can use any lens with focal length of the range 0.75cm to 12 cm.

(b) If the publisher wants to reduce the size to 1/15, them we need a magnification of 15.

then

when using the typical object distances, we get the range of focal lengths as 0.9375cm to 15cm