Answer to Question #126088 in Optics for Elshaddai

Question

A convex lens of focal length of 2cm is used to view an object of height 2mm. What is the angular magnification, position of the object and the height of the image if the final image is formed at the near point?

Answer 1

Angular magnification is

$$M=1+\frac{25\text{ cm}}{f}$$

Thus,$M=13.5$ .

As, given $f=2cm,v=-25cm$ and since

$$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\\\implies 1/2=-1/25-1/u\implies u=-50/27\approx1.85 cm$$

Since, image formed at near point, linear magnification is

$$m=M=h_i/h_o\implies h_i=Mh_o=2.7cm$$