Lecture 26 - Refraction at a curved surface 1 2...

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n 1 n 2 θ 1 θ 2 α β γ Refraction at a curved surface h/p=tan α α = θ 1 - γ = θ 1 -h/R h/i=tan β β = γ - θ 2 h/R=tan γ γ γ = θ 2 +b θ 1 = α + γ n 1 θ 1 -=n 2 θ 2 n 1 h/p+n 2 h/i=n 1 θ 1 -n 2 θ 2 +(n 2 -n 1 )h/R n 1 /p+n 2 /i=(n 2 -n 1 )/R
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A Lens • Suppose n 1 =1 (air), and we attach a second piece of concave transparent mirror to the first. Call R 1 and R 2 the radii of curvatures. • If we keep the pieces of glass thin, use the image of the first surface for the object for the second, and adopt the convention that if rays converge towards the object then we define the distance to be negative, then we get the lens makers formula: 1/o+1/i=(n-1)(1/R 1 -1/R 2 )=1/f . • Where 1/f=(n-1)(1/R 1 -1/R 2 ). • There is much that is useful here, especially if we pay attention to signs.
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Sign conventions • o>0 if rays diverge from the object. • i>0 if the image is on the opposite side of the lens than the object. • R>0 if the center of the circle is on the opposite side of the lens. • f>0 if the focal point is on the opposite side of the lens than the real object. • Note that a lens has two focal points that are positioned symmetrically.
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Lens Maker’s Formula, power, diopters 1/f=(n-1)(1/R 1 -1/R 2 ). • The quantity 1/f is called the power of lens.
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This note was uploaded on 05/11/2010 for the course PHY 214 taught by Professor Timothybolton during the Spring '10 term at Kansas State University.

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Lecture 26 - Refraction at a curved surface 1 2...

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