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502 Homework 2010 Set 10

502 Homework 2010 Set 10 - OPTI-502 Optical Design and...

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OPTI-502 Optical Design and Instrumentation I John E. Greivenkamp Homework Set 10 Fall, 2010 Assigned: 11/2/10 Lecture 21 Due: 11/9/10 Lecture 23 10-1) Design three different eyepieces for an optical system. All three eyepieces have a Magnifying Power of 10, and are to be used with a relaxed eye (the image presented to the eye is at infinity). The system objective presents an intermediate image to the eyepiece, and the intermediate pupil of the system is 200 mm to the left of this intermediate image plane. This intermediate pupil is the image of the stop through any optical elements between the stop and the eyepiece. a) A simple eyepiece consisting of just an eye lens. Determine the focal length and the eye relief. b) A compound eyepiece with a field lens located at the intermediate image plane. The field lens has a focal length of 40 mm. Determine the eye relief. c) A Ramsden-style eyepiece with the same eye relief as found with compound eyepiece of part (b). The field lens is located 12 mm to the right of the intermediate image plane. Determine the focal lengths of the two lenses and their separation. Hint: Three conditions must be met by the design -- the eyepiece must have the proper magnifying power, the final image presented to the eye must be at infinity, and the required eye relief must be obtained. 10-2) Eyeglasses are used when the focus of the eye does not fall on the retina. With myopia (nearsightedness), rays from a distant object focus in front of the retina. With hyperopia (farsightedness), these rays focus behind the retina. For the purposes of this problem, the eye can be modeled as a spherical refracting surface of index n. a) Eyeglasses are usually placed near the front focal point of the eye (assume they are at F). If φ g is the power of the eyeglasses and φ e is the power of the eye, what is the system power? b) Based on this answer, how do eyeglasses work? c) What happens if the eyeglasses are not at the front focal point of the eye? d) What is the sign of the power required to correct myopia and hyperopia?
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