Class8 - Read Hecht from Chapter 5 5.7 and Chapter 6...

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Comment: matrix for reflection and the sign for the elements of the ray vector = 1 1 1 1 2 2 2 2 1 0 1 Y n R n n Y n θ θ = 1 0 1 D R R n n D ) ( 1 2 = Refraction: (2) = 1 1 1 1 2 2 2 1 0 2 1 Y n R n Y n θ θ = 1 0 1 D M R n D 1 2 = Reflection: (3) (n=n 1 =-n 2 ) Note : “–” sign OK = 1 0 2 1 R n M Note : det(T)=det(R)=det(M)=1
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Comment: matrix for reflection and sign convention for angles Reflection matrix: Note the sign for the ray vector: n 1 θ 1 > 0 ( if θ 1 >0); while: n 2 θ 2 =-n 1 θ 2 < 0 Note: Hecht textbook uses n 1 =n 2 =n> 0 which implies a different form for the reflection matrix (see Hecht, eq. 6.39): = 1 0 2 1 ' R n M Note : det(M’)=-1 (4) Both forms of the reflection matrix (eq. 3 or eq. 4) are equally valid . Just keep in mind you have to use n=n 1 =-n 2 for the ray vector if you use eq. 3 and n=n 1 =n 2 if you use eq. 4. The advantage of eq. 3 is that it treats the reflection matrix in a similar way as the matrices for refraction and translation: det(M)=1, and 1/f=-a 12 = -2/R
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Comment: Thin Lens Equations 100 50 0 -100 -150 S i +10 cm S i +10 cm f S S i o 1 1 1 = + f=10 cm (positive lens) Image position S i Object position S o
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