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HW #12-solutions

# HW #12-solutions - Brannon(blb675 HW#12 Shih(58250 This...

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Brannon (blb675) – HW #12 – Shih – (58250) 1 This print-out should have 21 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points The thin composite lens has | R 1 | = R and | R 2 | = R 2 , as shown in the figure. R 1 R 2 n 2 n 1 The lens has focal length 1. f = n 2 n 2 - n 1 R . 2. f = n 1 4 ( n 1 - n 2 ) R . 3. f = n 2 2 ( n 1 - n 2 ) R . 4. f = n 1 2 ( n 2 - n 1 ) R . 5. f = n 1 n 1 - n 2 R . correct 6. f = n 2 n 1 - n 2 R . 7. f = n 1 n 2 - n 1 R . 8. f = n 2 2 ( n 2 - n 1 ) R . 9. f = n 1 2 ( n 1 - n 2 ) R . 10. f = n 1 4 ( n 2 - n 1 ) R . Explanation: Use the lens makers equation 1 f = n 2 n 1 - 1 1 R 1 - 1 R 2 = n 2 - n 1 n 1 1 R - 2 R = n 1 - n 2 n 1 1 R f = n 1 n 1 - n 2 R . 002 (part 1 of 2) 10.0 points A concave spherical mirror has a radius of cur- vature of 32 . 2 . The object distance is 8 . 2 cm . h q h p f R Scale: 10 cm = Find the magnitude of the image distance. Correct answer: 16 . 7114 cm. Explanation: 1 p + 1 q = 1 f = 2 R M = h h = - q p Concave Mirror f > 0 f > p > 0 -∞ < q < 0 > M > 1 Note: The radius of curvature for a concave mirror is positive, R = 32 . 2. Solution: Substituting these values into the mirror equation q = 1 1 f - 1 p = 1 2 R - 1 p = 1 2 32 . 2 - 1 8 . 2 cm = - 16 . 7114 cm | q | = 16 . 7114 cm . 003 (part 2 of 2) 10.0 points Find the magnification.

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Brannon (blb675) – HW #12 – Shih – (58250) 2 Correct answer: 2 . 03797. Explanation: M = - q p = - ( - 16 . 7114 cm) (8 . 2 cm) = 2 . 03797 . 004 (part 1 of 2) 10.0 points A convergent lens has a focal length of 25 cm . The object distance is 13 . 9 cm . f f q h p h Scale: 10 cm = Find the distance of the image from the center of the lens. Correct answer: 31 . 3063 cm. Explanation: 1 p + 1 q = 1 f M = h h = - q p Convergent Lens f > 0 f > p > 0 -∞ < q < 0 > M > 1 Note: The focal length for a convergent lens is positive, f = 25 cm. Solution: Substituting these values into the lens equation q = 1 1 f - 1 p = 1 1 (25 cm) - 1 (13 . 9 cm) = - 31 . 3063 cm | q | = 31 . 3063 cm . 005 (part 2 of 2) 10.0 points Find the magnification. Correct answer: 2 . 25225. Explanation: M = - q p = - ( - 31 . 3063 cm) (13 . 9 cm) = 2 . 25225 . 006 (part 1 of 3) 10.0 points Batman and Robin are attempting to escape that dastardly villain, the Joker, by hiding in a large pool of water (refractive index n water = 1 . 333). The Joker stands gloating at the edge of the pool. (His makeup is water- soluble.) He holds a powerful laser weapon y 1 = 1 m above the surface of the water and fires at an angle of θ 1 = 26 . 9 to the hori- zontal. He hits the Boy Wonder squarely on the letter “R”, which is located y 2 = 3 . 25 m below the surface of the water. θ x y y 1 1 2 R J Batplastic surface Mirrored Surface water B How far (horizontal distance) is Robin from the edge of the pool? (Fear not, Batfans. The “R” is made of laser-reflective material.) Correct answer: 4 . 89651 m.
Brannon (blb675) – HW #12 – Shih – (58250) 3 Explanation: Basic Concepts: Snell’s law, Total inter- nal reflection. Solution: Let x 1 be the horizontal distance from the laser to where the laser beam strikes the water and x 2 the horizontal distance from that point to Robin (see the following figure).

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HW #12-solutions - Brannon(blb675 HW#12 Shih(58250 This...

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