I've been doing some AAMC exams and Kaplan exams and have noticed some stuff on these exams about myopia and stuff... I know that nearsightedness is image converging in front of the retina, and thus a concave lens needs to diverge light onto the retina. And oppositely, a convex lens would converge light onto the retina in hyperobia... My question is where does the whole 1/o + 1/i = 1/f equation fit into all this? And where does the whole negative and positive sign convention fit in?
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In this case, 1/o + 1/i = 1/f isn't really the best equation to use to explain the answer to the question. To use that equation, we'd have to consider a two-lens system (the corrective lens and the person's own eye lens) and combine the two expressions before it really made sense. The one thing that does fit in is to remember that a converging species has a positive f, and a diverging species has a negative f. For lenses, a converging lens is a convex lens; a diverging lens is a concave lens.
To getter get a handle on what kind of lens we'd want, think about the very definition of a converging lens or diverging lens. A converging lens is so-called because it will refract parallel light rays to a given focal point. A diverging lens is so-called because it will refract parallel light rays as though they were all emanating from a given focal point. Converging lenses "pull" the light together, while diverging lenses "spread it apart".
If someone has hyperopia (farsightedness), it means that objects nearby tend to focus too far back in the eye, behind the retina (hence the prefix hyper- meaning "too much"). Adding a converging (convex) lens will cause the light to pull together closer to the lens -- it's converging it. For this person, that means that the image will begin to focus right on their retina.
This is also why contact lenses and glasses have those numbers. They represent the powers of the lenses, expressed in diopters. Remember that the power of a lens is calculated as 1/f. Thus, a converging (convex) lens will have a positive value for f, and a positive power. Farsighted people's lenses have positive values. Nearsighted people's lenses have negative values. The stronger the lens, the stronger an effect it has because it means that the focal length is getting closer and closer the the lens.
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In this case, 1/o + 1/i = 1/f isn't really the best equation to use to explain the answer to the question. To use that equation, we'd have to consider a two-lens system (the corrective lens and the person's own eye lens) and combine the two expressions before it really made sense. The one thing that does fit in is to remember that a converging species has a positive f, and a diverging species has a negative f. For lenses, a converging lens is a convex lens; a diverging lens is a concave lens.
To getter get a handle on what kind of lens we'd want, think about the very definition of a converging lens or diverging lens. A converging lens is so-called because it will refract parallel light rays to a given focal point. A diverging lens is so-called because it will refract parallel light rays as though they were all emanating from a given focal point. Converging lenses "pull" the light together, while diverging lenses "spread it apart".
If someone has hyperopia (farsightedness), it means that objects nearby tend to focus too far back in the eye, behind the retina (hence the prefix hyper- meaning "too much"). Adding a converging (convex) lens will cause the light to pull together closer to the lens -- it's converging it. For this person, that means that the image will begin to focus right on their retina.
This is also why contact lenses and glasses have those numbers. They represent the powers of the lenses, expressed in diopters. Remember that the power of a lens is calculated as 1/f. Thus, a converging (convex) lens will have a positive value for f, and a positive power. Farsighted people's lenses have positive values. Nearsighted people's lenses have negative values. The stronger the lens, the stronger an effect it has because it means that the focal length is getting closer and closer the the lens.
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