Question

Two rays traveling parallel to the principal axis strike a large plano-convex lens having a refractive index of 1.50 (see figure below). If the convex face is spherical, a ray near the edge does not pass through the focal point (spherical aberration occurs). Assume this face has a radius of curvature of R = 21.2 cm and the two rays are at distances h, = 0.500 cm and h, = 11.9 cm from the principal axis. Find the difference Ax in the positions where each crosses the principal axis. cm R

Answer 1

using snell's Love, nair sino2 =n sind, a = sint ensino, hair 02=sin(CIJA) The distance & 2 -hth tomo tomo k x 0-50 cm x =VR Ren where ø-02-0, Do R = 21.2 cm, n = 1.50 and the first yay is distance - 0.50cm. di = sint(0.50cm = 103514 2102cm Oz = sint (1-50(0-50)) = 2.0274% 1 2122 Ø = 02-0, = 0.676° x = √(21.2 cm) – 6.50cm) + tom (6.6769) * = 63.570cm Dt the second day is distance h2 = 11.9cm. o, = sin (11.) = 34.1422 Oz=sin" (1-50 (119))=57.34999 Ø = 02-0, = 2362027° x2 = 210 22 11090 11.9cm tom 23490270 = 45.30625 cm AX'=,-X=(63.570 - 45-30625) cm Ax = (18026 cm)