Question: A concave mirror forms an image on ascreen twice as large as the objec

Question

Question: A concave mirror forms an image on ascreen twice as large as the object. Both the object and the screenare then moved to produce an image on the screen that is threetimes the size of the object. If the screen is moved 75cm in theprocess, how far is the object moved? What is the focal length ofthe mirror? My Work:Well I have produced various answer using manydifferent equations such as 25cm moved, and 18.75 cm focalpoint. Using : and f = -s1.s/s-s1. The correct answers are 12.5 cm moved and75cm focal length. Any idea how to get those???m = -s1/s

Explanation / Answer

We know that magnification of the image formed by the concavemirror is m = hi / ho   = di/do hi = size of the image ho = size of the object Now hi = 2* ho         Then m = 2*ho / h o = 2           Then di= 2*do Now by the mirror formula   1/ f = 1/do + 1/di                                           1/f = 1/do + 1/2do                                           1/f = 3/2do    ---------(1) Where f is focal length of the concave mirror Now new magnification is m ' = 3 Now distance moved by the screen is x = 75cm Then new image distance di ' = di +x            new object distance do' =do-x'         m ' = di'/do' = di +x /do-x'          Then 3(do-x') = di +x Now 1/ f    = 1/do ' + 1/di'           1/ f = 1/do-x' + 1/di + x            1/f    = 1/ do-x' + 1/3(do-x') ---------(2) Solving 1 and 2 equations we get distance moved by the objectis x' = do /9           Nowagain solving 1 and 2 equations by putting the valuesof x and x' then we get object distance do =112.5cm           Thendistance moved by the object is x'= do/9 = 112.5cm /9 =12.5 cm        Now by solvingequation (1) by putting the value of do we get f = 75 cm .

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