DIVISION OF VISION SCIENCES SESSION: 2008/2009 2 ND DIET GEOMETRICAL OPTICS VISP103 LEVEL: 1 MODULE LEADER: DR HARRY ORBACH B.Sc/B.Sc. (HONS) OPTOMETRY AUGUST 2009 DURATION: 2 HOURS CANDIDATES SHOULD ATTEMPT FOUR QUESTIONS PLEASE READ THE QUESTIONS CAREFULLY Students for whom English is not their first language are permitted to use a Standard English/Foreign Language dictionary, e.g. French/English/English/French. Please ensure that the dictionary does not contain any notes or other materials and note that electronic dictionaries are not permissible MATERIALS TO BE SUPPLIED/ALLOWED: Lined Examination Script Books Unlined Examination Script Books Other Materials, e.g. Graph paper, statistical tables (please specify) GRAPH PAPER Question Paper Supplied) Calculator (Allowed) (but if calculator has full alphabet on keys confiscate) Page 1 of 6
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1. a) If the speed of light is 3x10 8 m/sec in air, and its speed in a block of glass is 1.9x10 8 m/sec, what is the refractive index of the block of glass? (2) b) What is the critical angle for light going from plastic with a refractive index of 1.4 into air with a refractive index of 1.0? (1) c) A circular opaque disc of diameter 24cm is 150cm from an extended source of light of diameter 30cm. Determine the length of the umbral cone. (4) d) A thin convex meniscus lens with radii of curvature +7.5cm and +15.0cm has refractive index 1.50. i) Determine the power of the lens (1) ii) Determine the positions of the principal foci (2) iii) A 30cm high object is placed 20cm in front of the lens. By drawing an accurate scale diagram, determine the position and size of the image. (6) e) Explain the terms "aperture stop" and "field stop". Illustrate with diagrams for the case of a simple convex lens. (4) 2. a) Light enters a flat surface of a transparent material, from air, at an angle of incidence of 45. If the angle of refraction, after entering the material, is 30º, determine the refractive index of the material. (2) b) Define the terms first focal point and second focal point. (2) c) Continued on next page c) Two prisms (one with apical angle ap = 30, the other with apical angle aq = 25 made of different types of materials (with refractive indices: np = 1.33 and nq = 1.7) Page 3 of 6
are arranged as illustrated in the following diagram: a p n q i a q n p For a pencil of parallel light rays with angle of incidence, i = 40, quantitatively calculate and illustrate the path taken by the light. (7) d) Using two rays from the tip of a real object, draw ray diagrams to illustrate image formation by a convex (positive) lens when a real object is: i) at three quarters the distance of the first focal length of the lens; (2) ii) at the first focal length of the lens; (2) iii) at a distance of 1.25 times the first focal length from the lens; (2) iv) Pick two of these cases and give an example of a practical application for each of these two optical arrangements. (3) 3. a) What is the visual angle subtended by a 5 ft tall object, 20 feet from the anterior surface of the cornea? (2) b) Determine the nominal and maximum magnifying powers of a convex lens of focal length 30cm. (2) c) Briefly describe (including a ray diagram) the optical system of a Keplerian (astronomical) telescope. (5) d) Prove that a ray goes through a glass block, in air, undeviated (i.e. the angle of refraction leaving the second surface equals the angle of incidence into the first surface). (3) e) What is the deviation produced by a thin prism of apical angle 2 made of glass of refractive index 1.5? (2) f) Derive the main law of reflection for flat surfaces. (You can use a derivation analagous to that for Snell s law.) (6) Page 4 of 6
4. a) Suppose that one can model a patient's eye as a single refracting surface of power +62.00D separating air from a medium with refractive index 4/3. i) Assuming there is no accommodation, if the axial length (from equivalent refracting surface to retina) of the eye is 22.22mm, at what distance would objects appear in focus? (4) ii) Assuming accommodation is relaxed, what condition does the patient have? (1) iii) What is the value for the far point of this patient's eye? (1) b) A room has a circular plane mirror of diameter 45cm mounted on its south wall. A point source of light is situated 1m from this mirror and on the normal to its centre. What is the diameter of the reflected light patch on a screen mounted on the room's north wall (3m from the south wall)? (3) c) Give one method for determining the focal length of a thin lens, including the appropriate equation with variables properly defined. (3) d) A concave mirror has radius of curvature -24cm. An object, 2cm high, is situated 16cm in front of the mirror. Using an accurate ray diagram, graphically determine the position, magnification and nature of the image. (8) 5. a). Explain, illustrating with diagrams which compare these conditions to normal, (emmetropic) vision, how myopia, hyperopia and presbyopia may arise. Indicate in which situations people with these conditions have normal vision and in which situations these conditions give rise to reduced visual acuity. (10) b) This question concerns the cardinal points: i) Using an illustrative diagram, define the meaning of the six cardinal points of an optical system. (6) ii) Find the cardinal points of a convex meniscus THIN lens, of index of refraction, 1.5, whose surfaces have radii of curvature of magnitude 80cm and 40cm. (4) END OF PAPER Page 5 of 6
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