Question

4. Show that the complex field transmittance, t of a double convex lens has the following form 1 + (x, y) h, exp-ik where 2f angle, q with respect Find the focus position if a plane wave is incident at an V (Bonus 5 points) prove the same result using ray optics. to the optical axis, Z.

Just only need to answer the bellow 2 question.

1.Find the focus position if a plane wave is incident at an angle, q with respect to the optical axis, z.

2.Prove the same result using ray optics.

Answer 1

Given that, f(x, y) = h_0 exp [- i k_0 x^2 + y^2/2f] where 1/f = (n - 1_(1/R - 1/R_2) For a double lens: - Here, Delta_0 = Thickness of a lens so, the phase retraditor b/w the tangent planes sigma and are Phi (x, y) = kn Delta (x, y)/lens + (Delta_0 - Delta_0 - Delta/air (x, y) If u_x (x, y) = field incident on the f^t plane, the field leaving, V_x (x, y) = t_r (x, y) U_l (x, y) where, t_l (x, y) = e^- Jk Delta_0 e^- JK (n - 1) Delta (x, y) Delta (x, y) = Delta, (x, y) + Delta_2 (x, y) Delta_1 (x, y) = Delta_01 - (R_1 - squareroot R^2_1 - x^2 - y^2) = Delta_0 - (R_1) (1 - squareroot 1 - x^2 - y^2/R^2_1 Delta_2 (x, y) = Delta_02 + R_2 (1 - squareroot 1 - x^2 + y^2/R^2_2 so, Delta (x, y) = Delta_0 - R_1 (1 - squareroot 1 - x^2 + y^2/R^2_1 + R_2 (1 - squareroot 1 - x^2/R_2 (Delta_0 Delta_02) By paraxial approx