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Designing an Achromatic Doublet, I Achromat The purpose is to give the same power for red and blue light. For touching two thin lens, we have the total power (red) $1,R + 2,R = 1.B + ₂B (blue) $₁,R Φ1,Β Φ2,Β - - - - (n₁,R − 1)P₁ + (n2,R − 1)P2 = (N₁,B − 1)P₁ + (n₂,B − 1) P₂ P₁ and P₂ are constant given by radii of curvatures. They do not depend on wavelengths 1 2 - P1 n2,B n2, R P2 n1,B1,R Condition for achromatic doublet: We can write this geometrical ratio in terms of the power at yellow light: Φ1,Υ Vd,1 P1 Q2,Y Va,² ₁,Y/(n₁,x - 1) $2,y/(n2x - 1) P2 Va,1 and Vd,2 are the Abbe numbers for the first lens and the second lens at d wavelength, respectively. since x (n-1) in lens-maker formula
Designing an Achromatic Doublet, 2 • In addition to the required condition shown on previous page, the powers of the two lenses should satisfy our desired overall power : Φ1,γ + Φ2,y = Φ ● Combining the two equations, we can solve for the power for each lens. • The analysis suggest that: O One lens has $₁,y > 0 and is made of a crown glass low dispersion (high Abbe number) - O The other has $2,y < 0 and is made of a flint glass - high dispersion (low Abbe number)
B4. You are asked to design a retarder plate that changes left-hand and right-hand circularly polarized light of wavelength 600.0 nm into two linearly polarized light polarized in x- and y-directions, respectively. A birefringent material is used, and it has the principal indices ne = 1.5533 and no = 1.5442 at wavelength 600.0 nm. (a) What should be the phase difference between the ordinary and extraordinary components? Explain the principle. (4 marks) (b) Find the minimum possible thickness of the retarder plate. (4 marks)