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lecture12 - Lecture 12 Notes 07 19 Simple Magnifier The...

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Lecture 12 Notes: 07 / 19 Simple Magnifier The simple magnifier consists of a single convergent lens. If an object is placed slightly inside the focal point of the lens, the image becomes much larger, but farther away. The observer can then position the eye so that the image is somewhere within the range of normal vision, between the near point and the far point: The image can be much larger than the object (infinite size if the object is at the focal point), but it is also farther away, so it will not necessarily subtend a much bigger angle with the eye and appear that much bigger. However, the lens allows the object to be held much closer to the observer than the observer's near point, since the lens will cause the virtual image to form beyond the near point; this causes the angle subtended by the image to in fact be larger than the angle subtended by the object at the near point. The angular magnification is defined as the angle subtended by the image, θ , divided by the angle, 0 , subtended by the object when it is at the near point without a lens: The angular magnification will depend on the focal length of the lens, the distance between the lens and the object p , the observer's near point p NP , and the distance between the lens and the observer's eye d . It can be calculated in a straightforward manner for any combination of these parameters. Here are some examples: Example: A lens with focal length f is held close to the eye ( d = 0) and used in such a way that the image forms at the eye's near point, p NP . What is the angular magnification? We want an image a distance of p NP behind the lens, so q = -p NP . From this, we can find the distance from the lens at which we should position the object, p :
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Now we need the size of the image compared to the size of the object. If the image size is h' and the object size is h , then The angle subtended by the object at the near point, with no lens, is (assuming the object is much smaller than the distance to the near point): When using the lens, the angle subtended by the image is The angular magnification is the ratio of the two angles: Note that this is only true if the lens is held very close to the eye, and at such a distance from the object that the image forms at the eye's near point. For example, suppose we have a magnifier with a focal length of 10 cm and an observer with a near point of 25 cm . Then, the angular magnification is m = 1 + 2.5 = 3.5. The image subtends an angle that is 3.5 times larger than the object, and so details 3.5 times smaller can be resolved. Example: An eye with normal distance vision is most relaxed when looking at an object at infinity. If we place the lens so that the image forms at infinity, what is the angular magnification? In order to form an image at infinity, the object is placed at the focal point.
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This note was uploaded on 09/19/2011 for the course PHYS 1C taught by Professor Smith during the Spring '07 term at UCSD.

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lecture12 - Lecture 12 Notes 07 19 Simple Magnifier The...

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