question_answer

The size of the image of an object, which is at infinity, as formed by a convex lens of focal length 30 cm is 2 cm. If a concave lens of focal length 20 cm is placed between the convex lens and the image at a distance of 26 cm from the convex lens, calculate the new size of the image

A) 1.25 cm

B) 2.5 cm

C) 1.05 cm

D) 2 cm

Correct Answer: B

Solution :

[b] Convex lens will form image \[{{I}_{1}}\] at its focus which acts like a virtual object for concave lens. Hence, for concave lens,\[u=+4cm\], \[f=20\]cm. so by lens formula \[\frac{1}{-20}=\frac{1}{v}-\frac{1}{4}\Rightarrow v=5cm\] i.e., distance of final image \[({{I}_{2}})\]from concave lens v=5 cm by using \[\frac{v}{u}=\frac{I}{O}\Rightarrow \frac{5}{4}=\frac{I}{2}\Rightarrow ({{I}_{2}})=2.5cm\]