Question

The focal lengths of the objective and of the eye-piece of a compound microscope are $f_0$ and $f_e$ respectively. If L is the tube length and D,the least distance of distinct vision, then find out its angular magnification, when the image is formed at infinity.

Answer 1

Hint
The focal length of a lens determines the magnification at which it images distant objects. It is equal to the distance between the image plane and a pinhole that images distant objects the same size as the lens in question. The magnification of a compound microscope is given by: m = where, D = Least distance of distinct vision L = Length of the microscope tube. $f_o$ = Focal length of the objective lens.

Complete step by step answer
According to the question , the focal length of the objective is $f_0$ and the eyepiece is $f_e$. The length of the tube is L. The least distance of distinct vision is D.
When, the image is formed at infinity
Then, $M = - \dfrac{L}{{{f_0}}}\dfrac{D}{{{f_e}}}$

Additional Information
Simple microscope's angular magnification formula is 1 + D/f, when the image is at D which is the least distance for distinct vision and it is D/f, when the image is formed at infinity. In the next video we will discuss a compound microscope.

Note
The angular magnification of a compound microscope is the ratio of the angle subtended by the final image at the eye to the angle subtended by the object at the eye, when both are placed at the least distance of distinct vision.