Question

A convex lens of focal length 0.12 m produces a virtual image which is thrice the size of the object. Find the distance between the object and the lens.
(A) 0.04m
(B) 0.08m
(C) 0.12m
(D) 0.24m

Answer 1

In this problem, we use the lens formula and the formula of magnification of a lens to calculate the object distance. The image distance can also be calculated accordingly but we need to only focus on the object distance in this case. The signs of focal length, object distance and image distance must also be kept in mind while solving such problems.

Formula used:
$\begin{aligned} & \dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u} \\\ & m=\dfrac{v}{u} \\\ \end{aligned}$

Complete step by step answer:
Given,
f=0.12m ($\because$ f is positive for a convex lens) ………. (1)
m=3
$\begin{aligned} & \Rightarrow \dfrac{v}{u}=3 \\\ & \Rightarrow v=3u \\\ \end{aligned}$ ……….. (2)
Plugging the values of (1) and (2) in the Lens formula, we have,
$\begin{aligned} & \dfrac{1}{0.12}=\dfrac{1}{3u}-\dfrac{1}{u} \\\ & \Rightarrow u=\dfrac{-2\times 0.12}{3} \\\ & \\\ \end{aligned}$
$\Rightarrow u=-0.08m$
Thus, the object distance is 0.08m. The negative sign is by the sign convention where the object distance is considered negative.

So, the correct answer is “Option B”.

Additional Information: A convex lens is also known as a positive lens or a converging lens. It converges rays of light parallel to it. The magnification is given by v/u and not –v/u unlike mirrors. These small differences in the formulas of mirrors and lenses must be noted so that that is no error in the calculations.

Note: The sign convention must be very clear while solving problems on mirrors and lenses. The new sign convention is used here. The object distance is considered negative in this case. The focal length is positive for a convex lens and negative for a concave lens. This must not be confused. Moreover, the magnification formula should be looked into properly as negative magnification means inverted image and positive magnification means erect image.