Question

When an object is placed on the principal axis of a convex lens at two different positions, it produces the images with magnification +2 and -4 respectively. How many times more away from the lens the image will be formed in the second position as compared to the first position?

• A. 2
• B. 4
• C. 5
• D. 10

Answer 1

Answer: (C)

5

Let there be two images at $v_1,v_2$ formed from two objects at $u_1,u_2$ by a lens of focal length $f$.

Thus $\frac{1}{v_1}=\frac{1}{u_1}+\frac{1}{f}$

And $\frac{1}{v_2}=\frac{1}{u_2}+\frac{1}{f}$

Now the magnification of first image is given by $\frac{v_1}{u_1}=+2$

Similarly $\frac{v_2}{u_2}=-4$

Substituting these values in above equations gives,

$\frac{v_2}{v_1}=-5$

Hence the two images are formed on opposite sides of the lens, with the second image 5 times farther than the first image from the lens.