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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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