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How come the microscope can allow us to see very very small things such as cells? Let's see how this optical system magnify those small images.
First, let's see how the image rays travels from the speicmen to the eyes.
From the above figure, we can see that the image rays get refracted when it enters and exits the objective lens and the eyepiece. From the start to the end, the ray start from a tiny point and it get magnified at the end at the human eyes. The ray got refract base on the index of refraction of the lens. These lenses are just illustrations. If we know the size of the lenses and the corresponding index of refraction then we can carry out a real ray tracing through math calculations.
From the above figure, we can understand how the image get magnified.
We consider an object OO'placed in front of the objective lens at a distance x1. Objective forms an inverted image I I1 at a distance of y1 from objective. Magnification of the objective is : Mo= x1/y1
The Eyepiece is like a magnifying glass, it furthers enlarge the image going through the objective lens. The magnification of the eyepiece is Me= x2/y2
Therefore, the magnifying power of the microscope is the linear magnification of the objective times the angular magnification of the eyepiece. We use angular magnification for the eyepiece because we are the image at conjugate. This means the light rays entering the eye are effectively parallel as would be experienced if the eye was focussed on an object at a great distance.
Magnification Power = Linear Magnification (Objective) * Angular Magnification (eyepiece)
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By James Chien-Chih Yeh 73976995