EN PH131 Chapter Notes - Chapter 12: Curve, Unit Vector, Cross Product

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amethystjellyfish251

21 Apr 2016

School

University of Alberta

Department

Engineering Physics

Course

EN PH131

Professor

Douglas Gingrich

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EN PH131 Full Course Notes

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Document Summary

Consider a particle which moves in a plane along a fixed curve, such that at a given instant it is at position s, measured from point o. The t axis is tangent to the curve at the point and is +ve in the direction of increasing s. +ve direction will be designated with the unit vector ut. A unique choice for the normal axis can be made by noting that geometrically the curve is constructed from a series of differential arc segments ds. Each segment ds is formed from the arc of an associated circle having a radius of curvature will be designated to as the curvature and center of curvature o". The normal axis n is perpendicular to the t axis w/ its +ve sense directed toward the center of. This +ve direction, which is always on the concave side of the curve, by the unit vector un.

Related Questions

a candle is placed in front of a convex mirror.

A candle is placed in front of a convex mirror.

Figure6 of 6The figure labeled C shows two rays coming out of the top of the object in front of the concave mirror, forming an acute angle with the axis. Upper ray reflects parallel to the axis. And the lower ray reflects in the direction exactly opposite to its initial direction. There is a focus point F on the axis in front of the mirror and a center of the mirror’s curvature C between point F and the object. The image is smaller, than the object, located between points F and C, and inverted, its tip is formed by intersection of the reflected rays. The initial upper ray passes through point F and the initial upper ray passes through point C. The figure labeled C shows two rays coming out of the top of the object in front of the concave mirror, forming an acute angle with the axis. Upper ray reflects parallel to the axis. And the lower ray reflects in the direction exactly opposite to its initial direction. There is a focus point F on the axis in front of the mirror and a center of the mirror’s curvature C between point F and the object. The image is smaller, than the object, located between points F and C, and inverted, its tip is formed by intersection of the reflected rays. The initial upper ray passes through point F and the initial upper ray passes through point C.

Part A Consider the following diagrams noting that the scale is different between diagrams. In these diagrams, C and F represent the center of curvature and the focal point of the convex mirror, respectively. The image formed by the mirror is obtained using the ray tracing technique. Which diagram(s) are correct?(Figure 1) (Figure 2) (Figure 3) Type A if you think that only diagram A is correct, type AB if you think that only diagrams A and B are correct, and so on.

Part B If the radius of curvature of the convex mirror is 50.0 cm , at what distance do from the mirror must the candle be placed so that its image is formed 20 cm from the mirror? Express your answer in centimeters. View Available Hint(s) dod o d_o = cm The convex mirror is now replaced by a concave mirror with the same radius of curvature.

Part C Consider the following diagrams, where now C and F represent, respectively, the center of curvature and the focal point of the concave mirror. Again, the image formed by the mirror is found by ray tracing. Choose the correct diagram(s).(Figure 4) (Figure 5) (Figure 6) Type A if you think that only diagram A is correct, type AB if you think that only diagrams A and B are correct, and so on. View Available Hint(s)

Part D Assuming that the candle remains at a distance do from the mirror (the same distance found in Part B), at what distance di from the mirror will its image form now? Express your answer in centimeters. View Available Hint(s) did i d_i = nothing cm