University:
Massachusetts Institute of Technology
Course:
2.71 | Optics
Academic year:

2020
Views:

325

Pages:

11
Author:

Kiley Moore

MASSACHUSETTS INSTITUTE OF TECHNOLOGY 2.71 Optics Solutions to Problem Set #3 Problem 1: Wanda's world. a) The geometry for this problem is shown in Figure 1. For part (a), the object (Wanda) is located inside the bowl and we are interested to find where the image is formed. We start by using the matrix formulation to analyze the given system, (2-1) 10 720 To (1) = 지 1 (1-) +1+ 1- R To find the imaging condition, we note that all the rays, regardless of their departure angle o, arrive at the image point z, (ie. Dr/da, = 0), R n + 8 = 0 = -R. (2) We see that the image is formed at the center of the bowl and is virtual. Using this result in equation 1, 0 (3) The lateral magnification is. M= (4) and therefore, the image is erect. b) For this part, the object (Olive) is located outside the bowl and we are interested to find where the image is formed. Again, we solve this part using the matrix formulation, (n-1) 21 To 1- +8 (n-1) (0-1) mat = (-1) 1- 1 (5) From the imaging condition (dz/da, 0), we solve for s', +8 88 (n-1) R 8 = = 0 (6) snR s(n-1)-R The lateral magnification is (for an on-axis ray, a = 0). M 1- s(n-1) R sn.R (n-1) (s(n-1)-R)nR 1- R s(n-1)-R From equations 6 and 7, the following cases arise: 1. If Rs(n-1)<0, the image is virtual, erect and is located at a distance s outside the bowl. 2. If Rs(n-1)>0, the image is real, inverted and is located at a distance inside the bowl. c) If we were to consider the glass container of thickness & as well as the inner, R₁, and outer, R₂, radii, the matrix formulation becomes, 1 To (8) 1 R P Rang 1 1+Ps- P πα = (1- P---)(-1)]. R + R where, (9) For the case of uniform glass: RRR. The imaging condition is, 88 (n-1) st(-ng) R Run + 1st (2-1) Rng + (n-1) Rng R 2 (7) b) If we place a small object at s_o in front of L1, the instrument acts as a microscope. The magnifying power, MP, is the ratio of the image size formed on the human's retina when using the instrument and the image size when viewed with the naked eye, MP = (M_L1 * M_A1 * 254) / 20 = (170 / 10.625) * (254 / 20) = 203X. where, M_L1 is the lateral magnification of the objective (L1) and M_A1 is the angular magnification of the eyepiece (L3).

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