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Lecture15

# Lecture15 - Lecture 15 Images from Lenses Last lecture we...

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Last lecture we discusses the image formed by a spherical mirror: And derived the mirror equation: 1 s + 1 σ = 2 Ρ = 1 φ y object y s f R Lecture 15: Images from Lenses

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Lenses Refraction can also be used to form images Let’s assume an object is in material with index of refraction n 1 Some rays then enter material with larger index of refraction n 2 Boundary between two materials is spherical R n 2 n 1 s Object Image
As with the spherical mirror, we’ll only consider paraxial rays (rays that are almost parallel to the principal axis) As shown on the previous page, all paraxial rays starting from the object meet at the image position We can consider just one off-axis ray to work out the geometry: R n 2 n 1 Object Image θ 1 α β γ θ 2 R s d

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From Snell’s Law, we know that But since we’ve made the assumption that all angles are small, this becomes We also see that: 2 2 1 1 sin sin θ θ ν ν = 2 2 1 1 θ θ ν ν = α + β + 180 o - q 1 ( ) =180 o q 1 = a + b q 2 + 180 o - b ( ) + g =180 o b = q 2 + g
We can now substitute in for Snell’s Law: Looking at the triangles on our diagram (and keeping in mind that all the angles are small!) we find that: Plugging into the Snell’s Law equation, we find:

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