Mathematics of Microscope Resolving Power :: Math

Missing Figures Imagine this, you are walking through the forest when all of a sudden you come across the most fascinating insect (perhaps insects may not seem too fascinating at first but once you learn a little about them they are the most fascinating creatures). Well, back to the story, so you find this insect and you realize that it seems very different from those you've previously encountered. Well, being the curious scientist that you are, you take out your trusty magnifying glass and take a look. You move the lens back and forth until you find the perfect image. You see the insect's wonderful colours and patterns which you would not be able to see with your naked eye. What just happened? You simply placed a piece of glass between you and the insect and all of a sudden you get this wonderful view of nature which would otherwise be missed. Well, if you are at all curious as to know how magnifying glasses and microscopes work, then read on and find out. An Introduction to Microscopes The two types of microscopes that will be focused on in this webpage are the simple microscope and the compound microscope. The simple microscope, also known as the magnifying glass, is composed of a single converging lens. The compound microscope is composed of at least two lenses and is generally referred to as a microscope. There are two main purposes of a microscope: 1) to increase the magnification of an object 2) to have a high resolving power Both of these will be examined; however, a greater emphasis will be placed on the resolving power. Magnifying Power (brief overview) Magnifying power: is also called angular magnification. Figure 1a shows an object y in front of a lens. Rays of light reflect off the object through the lens and a now larger image, y', of y can be seen. Once, the image is brought further from the lens, as in figure 1b, the image, y', is even larger. (So as to no discrepency: in figures 1a and 1b, the observer is on the right of the lens looking towards the image y') The magnifying power, M, is given by the following: M = 1 + d/f, where f is the focal distance and d is the distance between the object and the lens Proof of M = 1 + d/f: Figure 1c is the view of the object Y from point C without a magnifying glass. Mathematics of Microscope Resolving Power :: Math Missing Figures Imagine this, you are walking through the forest when all of a sudden you come across the most fascinating insect (perhaps insects may not seem too fascinating at first but once you learn a little about them they are the most fascinating creatures). Well, back to the story, so you find this insect and you realize that it seems very different from those you've previously encountered. Well, being the curious scientist that you are, you take out your trusty magnifying glass and take a look. You move the lens back and forth until you find the perfect image. You see the insect's wonderful colours and patterns which you would not be able to see with your naked eye. What just happened? You simply placed a piece of glass between you and the insect and all of a sudden you get this wonderful view of nature which would otherwise be missed. Well, if you are at all curious as to know how magnifying glasses and microscopes work, then read on and find out. An Introduction to Microscopes The two types of microscopes that will be focused on in this webpage are the simple microscope and the compound microscope. The simple microscope, also known as the magnifying glass, is composed of a single converging lens. The compound microscope is composed of at least two lenses and is generally referred to as a microscope. There are two main purposes of a microscope: 1) to increase the magnification of an object 2) to have a high resolving power Both of these will be examined; however, a greater emphasis will be placed on the resolving power. Magnifying Power (brief overview) Magnifying power: is also called angular magnification. Figure 1a shows an object y in front of a lens. Rays of light reflect off the object through the lens and a now larger image, y', of y can be seen. Once, the image is brought further from the lens, as in figure 1b, the image, y', is even larger. (So as to no discrepency: in figures 1a and 1b, the observer is on the right of the lens looking towards the image y') The magnifying power, M, is given by the following: M = 1 + d/f, where f is the focal distance and d is the distance between the object and the lens Proof of M = 1 + d/f: Figure 1c is the view of the object Y from point C without a magnifying glass.