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HW25soln - Physics 21 Fall 2007 Solution to HW-25...

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Physics 21 Fall 2007 Solution to HW-25 Understanding Spherical Mirrors Consider a concave spherical mirror with a radius of curvature equal to 60.0 cm. An object 6.00 centimeters tall is placed along the axis of the mirror, 45.0 centimeters from the mirror. You are to find the location and height of the image. (A) What is the focal length f of this mirror? 30 cm (half the radius of curvature) (B) Now use the spherical mirror equation to find the image distance d _i. 1/ d _i = 1/ f - 1/ d _o = 1/30 - 1/45 = 1/90, so f = 90 cm. (C) Find the magnification m , using d _o and d _i. m = - d _i/ d _o = -90/45 = -2.00 (D) Finally, use the magnification to find the height of the image. h _i = m h _o = -2.00 (6.0 cm) = -12.0 cm (E) Look at the signs of your answers to determine which of the following describes the image formed by this mirror: real and inverted since m < 0 and image is in front of mirror (F) Solve the spherical mirror equation for d _i. 1/ d _i = 1/ f - 1/ d _o =( d _o - f )/( f d _o) => d _i = ( f d _o)/( d _o - f ) (G) What is the magnification m ? Use your answer from Part F. m

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HW25soln - Physics 21 Fall 2007 Solution to HW-25...

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