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The lens formula

Answer Text:
The lens formula
Let the object distance be represented by ‘u’, the image distance by ‘v’ and the focal length by ‘f’, then the general formula relating the three quantities is given by;
#1 / f = 1 / u + 1 / v #– this is the lens formula.
Examples
1. An object is placed 12 cm from a converging lens of focal length 18 cm. Find the position of the image.
Solution
Since it is a converging lens f =+18 cm (real-is-positive and virtual-is-negative rule)
The object is real therefore u = +12 cm, substituting in the lens formula, then
#1 / f = 1 / u + 1 / v or 1 / v = 1 /f – 1 / u = 1 / 18 – 1 / 12 = - 1 /36#
Hence v = - 36 then the image is virtual, erect and same size as the object.
2. The focal length of a converging lens is found to be 10 cm. How far should the lens be placed from an illuminated object to obtain an image which is magnified five times on the screen?
Solution
f = + 10 cm #m = v / u #= 5 hence
v = 5 u
Using the lens formula 1 / f =
#1 / u + 1 / v = 1 /10 = 1 / u + 1 / 5u #(replacing v with 5 u)
#1 / 10 = 6 / 5u#, hence 5 u = 60 giving u = 12 cm (the lens should be placed 12 cm from the illuminated object)