Find the two locations where an object can be placed in front of aconcave mirror

Question

Find the two locations where an object can be placed in front of aconcave mirror with a radius of curvature of 41 cm such that its image is three times its size. In each of these cases,state whether the image is real or virtual, upright or inverted. location (cm) real or virtual orientation closer position ? ? upward or inverted? farther position ? ? upward or inverted? location (cm) real or virtual orientation closer position ? ? upward or inverted? farther position ? ? upward or inverted? location (cm) real or virtual orientation closer position ? ? upward or inverted? farther position ? ? upward or inverted?

Explanation / Answer

Given : .                Radius of curvature (R) = 41 cm .                 ==> focal length (f) = R / 2 = 41/2 = 20.5 cm .                 Magnification is : M = - v / u =  ± 3   .                                                ==>   v  =  ± 3 u .                From Len's maker's formula we have : .                        1 / f   = 1 / u + 1 / v .             or        1 / 20.5 = 1 /u  ± 1 / 3u . For negative sign : .             or        1 / 20.5 = 1 / u [ 1 - 1/3 ] .             or        1 / 20.5 =  0.667 / u .             or           u        = 0.667 *20.5 = 13.675 cm . For positive sign : .             or        1 / 20.5 = 1 / u [ 1 + 1/3 ] .             or        1 / 20.5 =  1.334 / u .             or           u        =  1.334* 20.5 =  27.347 cm . Hence Image upward near farther position. . Hope this helps u! For positive sign : .             or        1 / 20.5 = 1 / u [ 1 + 1/3 ] .             or        1 / 20.5 =  1.334 / u .             or           u        =  1.334* 20.5 =  27.347 cm . Hence Image upward near farther position. . Hope this helps u!

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