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Acids, Bases And Salts

Question
CBSEENSC10014820

A 5 cm tall object is placed perpendicular to the principle axis of a convex lens of focal length 12 cm. The distance of the object from the lens is 8 cm. Using the lens formula, find the position, size and nature of the image formed.

Solution

Given,
Object distance from the lens, u = - 8 cm
Focal length of the lens, f = 12 cm
Height of the object, h = 5 cm
Using the lens formula,
1 over straight v minus 1 over u equals 1 over f
Putting the values,
1 over straight v equals 1 over 12 plus fraction numerator negative 1 over denominator 8 end fraction
space space space space equals space 1 over 12 minus 1 over 8
space space space space equals space fraction numerator 2 minus 3 over denominator 24 end fraction
space space space space equals space fraction numerator negative 1 over denominator 24 end fraction

rightwards double arrow space v space equals space minus 24 space c m
Thus, image is formed 24 cm on the left of the convex lens.
That is, object is formed on the same side of the object.
Now,
Magnification, m = straight v over straight u equals fraction numerator h apostrophe over denominator h end fraction equals fraction numerator negative 24 over denominator negative 8 end fraction equals fraction numerator h apostrophe over denominator 5 end fraction
That is,
Height of the image, h' = 15 cm (positive)
Height of the image is 15 cm which is 3 times larger than the height of the object.
Therefore, the image formed is virtual, enlarged and erect.