A convex lens forms an 8.0 cm long image of a 2.0 cm long object which is kept at a distance of 6.0 cm from…
A convex lens forms an 8.0 cm long image of a 2.0 cm long object which is kept at a distance of 6.0 cm from the optical centre of the lens. If the object and the image are on the same side of the lens, find (i) the nature of the image, (ii) the position of the image, and (iii) the focal length of the lens.
Solution
(i) Nature: Virtual and erect
(ii) Given h' = + 8.0 cm, h = + 2.0 cm, u = – 6 cm
m = h'/h = v/u
= 8.0cm/2.0cm = v/–6 cm
or v = – 24 cm
Thus, the image is at a distance of 24 cm from the lens.
(iii) Lens formula $\dfrac{1}{v}$ – $\dfrac{1}{u}$ = $\dfrac{1}{f}$
1/–24 – 1/–6 = $\dfrac{1}{f}$
–1/24 + 1/6 = $\dfrac{1}{f}$
1/8 = $\dfrac{1}{f}$
f = 8 cm
Thus the focal length of the lens = 8 cm