Lecture-23-04-08-08

# Lecture-23-04-08-08 - 1 Parallel lines Lecture-23...

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Unformatted text preview: 1 Parallel lines Lecture-23 Geometrical Optics- continued • Lensmaker’s equation Snell’s law gives and Also from figure, we have Or , For thin lens we obtain Lensmaker’s equation : Note that R 1 > 0 if center of curvature is on right, and R 2 > 0 if on left, of lens. 2 1 2 1 4 3 ) ( θ θ β α θ θ θ γ θ α + − + = − − = − = n n n 1 1 1 1 2 2 2 2 2 nR h R h nf h nR h R h + − + = 2 1 θ θ γ − = R 2 R 1 2 1 θ θ n ≈ 3 4 θ θ n ≈ ; sin 1 1 1 1 R h = ≈ θ θ f h and R h 2 2 2 ; ≈ ≈ β α . , 1 1 ) 1 ( 1 2 1 2 1 h h where R R n f ≈ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + − = 2 f d d L i i 1 1 1 = + − 2 = + − Lf Ld d i i L ( ) ( ) f d d i o 1 1 1 = + • Thin lens equation Δ ABF is similar to Δ II ’ F , and therefore Also Δ OO’A is similar to Δ II’A , and thus Thus Lens’ equation: • Lens’ equation is quadratic in d i : Set L= d o + d i , then Or, and the roots are There are two sharp-focus lens positions for given L :- One magnified and...
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Lecture-23-04-08-08 - 1 Parallel lines Lecture-23...

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