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At small angles, refraction of light off a spherical surface of radius R between mediums with indices of refraction n1 and n2 is given by n, n2 // Image Obiect n1 n2 n2 - n1 R where o is the object's distance from the spherical surface and i is the image's dis- tance, and o is in medium n1 and i is in medium n2. If the spherical surface is curved in the direction depicted in the first diagram, then R> 0. If the surface is curved in the other direction, then R< 0. The sign conventions of o and i are the same as those of the thin lens equation that

At small angles, refraction of light off a spherical surface of radius R between mediums with indices of refraction n1 and n2 is given by n, n2 // Image Obiect n1 n2 n2 - n1 R where o is the object's distance from the spherical surface and i is the image's dis- tance, and o is in medium n1 and i is in medium n2. If the spherical surface is curved in the direction depicted in the first diagram, then R> 0. If the surface is curved in the other direction, then R< 0. The sign conventions of o and i are the same as those of the thin lens equation that

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At small angles, refraction of light off a spherical surface of radius R between n, // mediums with indices of refraction n1 and nz n2 is given by n2 - n1 Object Image n1 n2 where o is the object's distance from the spherical surface and i is the image's dis- tance, and o is in medium n1 and i is in medium n2. If the spherical surface is curved in the direction depicted in the first diagram, then R> 0. If the surface is curved in the other direction, then R< 0. The sign conventions of o and i are the same as those of the thin lens equation that you're used to. (a) Now consider a thin lens of thick- ness d and index of refraction n surrounded by air (nair both surfaces need not have the same mag- 1). The radii Rị and R2 of nitude. By treating the lens as a combina- tion of two instances of the above equation what does 1 1 equal to? Answer in terms of the n, R1, and R2. Use the approximation that d is negligibly small to solve this problem. (b) The focal length of a lens is defined as the reciprocal of the answer you found in the previous part. The lens in the diagram is a biconvex lens. Is a biconvex lens converging or diverging? What about a biconcave lens?
Transcribed Image Text:At small angles, refraction of light off a spherical surface of radius R between n, // mediums with indices of refraction n1 and nz n2 is given by n2 - n1 Object Image n1 n2 where o is the object's distance from the spherical surface and i is the image's dis- tance, and o is in medium n1 and i is in medium n2. If the spherical surface is curved in the direction depicted in the first diagram, then R> 0. If the surface is curved in the other direction, then R< 0. The sign conventions of o and i are the same as those of the thin lens equation that you're used to. (a) Now consider a thin lens of thick- ness d and index of refraction n surrounded by air (nair both surfaces need not have the same mag- 1). The radii Rị and R2 of nitude. By treating the lens as a combina- tion of two instances of the above equation what does 1 1 equal to? Answer in terms of the n, R1, and R2. Use the approximation that d is negligibly small to solve this problem. (b) The focal length of a lens is defined as the reciprocal of the answer you found in the previous part. The lens in the diagram is a biconvex lens. Is a biconvex lens converging or diverging? What about a biconcave lens?
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