Reflection and Mirrors - Mission RM7 Detailed Help

A Chinese magician named Foo Ling Yu uses a concave mirror with a 48.4-cm focal length in order to perform a magic trick. Foo places a 2.8-cm wide coin a distance of 99.1 cm from the mirror. What is the image distance and the image width of the coin? (Enter a POSITIVE number.)

The mirror equation relates the object distance (d_o), the image distance (d_i) and the focal length (f):

1 / d_o + 1 / d_i = 1 / f

The magnification equation relates the magnification (M), object height (h_o), the image height (h_i), object distance (d_o) and the image distance (d_i):

M = h_i / h_o = - d_i / d_o

The magnification value is an expression of the number of times bigger that the image height is than the object height.

There are two unknowns to determine in this question - the image distance and the image width (comparable to image height). Use the mirror equation to first determine the image distance. See the Math Magic section if necessary.

Once you've calculated the image distance, use the magnification equation to determine the image height. For a circular coin, it's height is the same as its width. You will have to equate the ratio of image and object heights to the ratio of image and object distances. There is a negative sign as part of the equation. The image height should turn out to be a negative value, indicating an inverted image. Enter the answer as a POSITIVE value - absolute value only. See Formula Frenzy section.

It is important that you do not use rounded numbers in any calculation. Enter both answers to at least the second decimal place. See A Very Fine Detail section.

The mirror equation, with its three reciprocal terms, is a little awkward to work with. It's recommended that you begin this problem by performing an algebra step to rearrange the equation such that the image distance (the unknown) is by itself on the left side of the equation. Then substitute the two numerical values into the equation and use your calculator to evaluate the right side. Once done, the reciprocal of the image distance is equal to the number on your calculator. Take the reciprocal of this number to determine the image distance.

The Minds On Physics program calculates answers accurate to the fourth decimal place. Your answer does not need to be that accurate. The program will allow you to have a 1 percent deviation from the right answer without being wrong. This means two things: 1) Enter your answer with at least three significant digits. 2) Do not round any numbers until your final calculation.

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