Answer to Question #167251 in Optics for Olufemi george

Question

A converging thin lens with 50cm focal lens forms area/image that is 2.5 times larger than the object. How Far is the object from the image.

Answer 1

Let's write the magnification equation:

$$M=\dfrac{2.5h_i}{h_0}=-\dfrac{d_i}{d_0},$$ $$2.5=-\dfrac{d_i}{d_0},$$ $$d_i=-2.5d_0.$$

Let's write the thin lens equation and find the object distance:

$$\dfrac{1}{d_o}+\dfrac{1}{d_i}=\dfrac{1}{f},$$ $$\dfrac{1}{d_o}-\dfrac{1}{2.5d_o}=\dfrac{1}{f},$$ $$d_o=\dfrac{1.5f}{2.5}=\dfrac{1.5\cdot50\ cm}{2.5}=30\ cm.$$

Then, we can find the image distance:

$$d_i=-2.5d_0=-2.5\cdot30\ cm=-75\ cm.$$

The sign minus indicates that the image is virtual and formed on the same side as the object.

Finally, we can find the distance from the object to the image:

$$d=d_i-d_o=75\ cm-30\ cm=45\ cm.$$

Hence, the image formed 45 cm to the left from the object.