Answer to Question #153933 in Optics for Adepoju Ireoluwa

Question

Find the magnification of the image formed by a lens of 5 dioptres when the object is 20m away from it

Answer 1

Solution. According to the condition of the problem focal distance

$$F=\frac{1}{D}=\frac{1}{5}=0.2m$$

Using the thin lens equation

$$\frac{1}{o}+\frac{1}{i}=\frac{1}{F}$$

where o=20m is object distance; i is image distance. Therefore

$$\frac{1}{i}=\frac{1}{F}-\frac{1}{o}$$

$$i=\frac{o\times F}{o-F}=\frac{0.2\times20}{20-0.2}=\frac{4}{19.8}\approx 0.202m$$

Sketch the image

Using definition the magnification

$$M=\frac{h_i}{h_o}=\frac{i}{o}=\frac{0.202}{20}\approx 0.01$$

Answer. 0.01