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615.


Problem 44.17 (RHK)


We have a supply of flat glass disks and a lens grinding machine that can be set to grind radii of curvature of either 40 cm or 60 cm. We are advised to prepare a set of six lenses like those shown in the figure. We have to find the focal length of each lens. (Note: Where we have a choice of radii of curvature, we will select the smaller one.)

Solution:           Click For PDF Version

We will use the lens-maker’s formula

,

and the sign convention that is positive if the centre of curvature lies in the R-side of the lens and is negative if the centre of curvature lies in the V-side of the lens.

Also, the radius of curvature of a plane surface is .

In the following we calculate the focal length of the six lenses shown in the figure:

(a)

Double convex lens

.

We have

(b)

Planar convex

.

We have

(c)

Meniscus convex

.

We have

(d)

Double concave

We have

(f)

Planar concave

.

We have

(g)

Meniscus concave

.

We have