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Unformatted text preview: arango (da2356) – HW02 – markert – (58710) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A C N P B D Which of the glass lenses above, when placed in air, will cause rays of light (par- allel to the central axis) to diverge ? 1. B, D, C, and A 2. D and C 3. D and P correct 4. B, D, and P 5. N and C 6. B, P, and A 7. B, N, and P 8. B, C, and A 9. B, N, and C 10. B, D, N, and A Explanation: convergent divergent Use the lens makers’ equation 1 f = ( n- 1) parenleftbigg 1 R 1- 1 R 2 parenrightbigg , where R 1 and R 2 are + (or- ) if the center of curvature is behind (or in front of) the lens. To cause parallel rays of light to converge, f must be positive, ( n > 1). B: R 1 > 0 and R 2 = ∞ , = ⇒ f > , therefore convergent. D: R 1 = ∞ and R 2 > 0, = ⇒ f < , therefore divergent. N: R 1 > 0 and R 2 > 0, but | R 1 | > | R 2 | , = ⇒ f > , therefore convergent. P: R 1 < 0 and R 2 < 0, but | R 1 | < | R 2 | , = ⇒ f < , therefore divergent. C: R 1 < 0 and R 2 < 0, but | R 1 | > | R 2 | , = ⇒ f > , therefore convergent. A: R 1 > 0 and R 2 > 0, but | R 1 | = | R 2 | , = ⇒ f = ∞ , therefore neither convergent or divergent. Thus, lenses B, N, and C are convergent lenses and Lenses D and P are divergent. Alternate (Elegant) Solution: Converging Lens: The glass is thicker on the axis than at the edge. B, N, and C satisfy these conditions for a converging lens ( f > 0). Diverging Lens: The glass is thinner on the axis than at the edge. D and P satisfy these conditions for a di- verging lens ( f < 0). Neutral Lens: The glass has a constant thickness. Rays of light are parallel to the central axis on both sides of the lens. A satisfy this conditions for a non-focusing lens ( f = ∞ ). Digression based on Huygen’s principle: Consider the passage of a wave front of a plane wave through a lens. If the center part of the lens is thicker, the center of the exit vertical plane has a larger phase change compared to that in the region surrounding the center. So the surrounding region needs to travel farther to acquire the same phase change. Analogously, if the lens at the center is thinner, at the exit side the center part needs to travel farther to acquire the same phase as that in the peripheral region. This leads to a divergent wave front at the exit side of the lens. arango (da2356) – HW02 – markert – (58710) 2 002 10.0 points If the object distance for a converging thin lens is more than twice the focal length of the lens, the image is 1. located at a distance between f and 2 f from the lens. correct 2. virtual and erect. 3. located at a distance more than 2 f from the lens....
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- Spring '07
- Thin lens, Dioptre