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UW-Madison PHYSICS 104 - Discussion Notes - Conceptual Problem 2

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Discussion Notes for July 21st, 2008Conceptual Problem #2In a Jules Verne novel, a piece of ice is shaped into a magnifying lens to focus sunlight to start a fire. Is this possible?In theory the ice is the same as a lens and because its index of refraction is greater than that of air (about 1.3) it could start a fire. However, in real life the ice would melt.Quantitative problem #1A concave makeup mirror is designed so that a person 25 cm in front of it sees an upright image magnified by a factor of two. What is the radius of curvature of the mirror? P = 25 cm F object image The following values are given M = +2 P = 25 cm From these values we can calculate q from the equation M=-q/p 2 = -q/25 q = -50 Than plug in the p and q values to the equation below and solve for R (radius of curvature) 1/p + 1/q = 2/R 1/25 + 1/-50 = 2/R R = 100 cmq = -50Quantitative problem 1 modified:A divergent lens is placed 25 cm away from a concave mirror with an object directly between them. The radius of curvature is 20 cm and the focal length of the lens is 16.7 cm. Find the location of the image and determine if it is real/virtual, upright/inverted, and its magnification First you need to find the distance of the image from the mirror 1/p + 1/q = 2/R 1/12.5 = 1/q = 2/20 q = 50 cm Next use the image as an object to find the distance from the lens of the new image 1/p + 1/q = 1/f 1/25 + 1/q = 1/-16.8 q = -50.3 Than find the magnification M total = M mirror * M lens M = (-q/p) * (-q/p) M = + 8.05  A positive magnification means that the image is upright The image is virtual, upright and has a magnification of 8.05Inference – two waves that add constructively or destructively. Constructive waves have a phase difference that is a multiple of λ. Destructive waves have a phase difference which is a multiple of λ/2.Quantitative Problem #2:In a location where the speed of sound is 354 m/s, a 2000-Hz sound wave impinges on two slits30.0 cm apart. (a) At what angle is the maximum located? (b) If the sound wave is replaced by3.00-cm microwaves, what slit separation gives the same angle for the first maximum? (c) If theslit separation is 1.00 micrometer, what frequency of light gives the same first maximum angle? a). Use the speed of light and the frequency to find the wavelength v = f λ λ = .117 Than find the angle at maximum D sin θ = mλ θ = 36.2 b). Use the maximum angle for new separation distance d sin 36.2 = 1 * .03d = 5.08 m c). Find the Frequency using v/f for wavelength d sin θ = m (v/f) f = 6 x


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