(a) An object 2 cm tall stands on the principal axis of a converging lens of focal length 8 cm. Find the position, nature and size of the image formed if the object is :
(i) 12 cm from the lens
(ii) 6 cm from the lens
(b) State one practical application each of the use of such a lens with the object in position (i) and (ii).
(a) \(h_1\) = 2 cm
f = 8 cm
(i) u = -12 cm
\(\frac{1}{v}\) - \(\frac{1}{u}\) = \(\frac{1}{f}\)
\(\frac{1}{v}\) - \(\frac{1}{-12}\) = \(\frac{1}{8}\)
\(\frac{1}{v}\) = \(\frac{1}{24}\)
v = 24 cm
Image is 24 cm behind the lens.
m = \(\frac{v}{u}\) = \(\frac{h_2}{h_1}\)
\(\frac{24}{-12}\) = \(\frac{h_2}{2}\)
\(h_2\) = -4 cm
Image is 4 cm high, real and inverted.
(ii) u = -6 cm
\(\frac{1}{v}\) - \(\frac{1}{u}\) = \(\frac{1}{f}\)
\(\frac{1}{v}\) - \(\frac{1}{-6}\) = \(\frac{1}{8}\)
\(\frac{1}{v}\) = -\(\frac{1}{24}\)
v = -24 cm
Image is 24 cm in front of the lens.
m = \(\frac{v}{u}\) = \(\frac{h_2}{h_1}\)
\(\frac{-24}{-6}\) = \(\frac{h_2}{2}\)
\(h_2\) = 8 cm
Image is 8 cm high, virtual and erect.
(b) (i) Used in film projector.
(ii) Used as a magnifying glass.