A concave mirror has a radius of curvature of 8.2 cm. (a) Determine the object p

Question

A concave mirror has a radius of curvature of 8.2 cm. (a) Determine the object position for which theresulting image is upright andsix times the size of the object.

Your answer is within 10% of the correctvalue. This may be due to roundoff error, or you could have amistake in your calculation. Carry out all intermediate results toat least four-digit accuracy to minimize roundoff error.cm
The problem states that it is wrong, but I don't understandwhy. Here is what I did 1/p + 1/q = 2/R R= 8.2cm Bc resulting image is upright and six timesthe size of the object.     * q= -6p Thus 1/p + 1/ (-6p) = 2/R    5/6p = 2/R    5/6p= 2/8.2cm    p = 3.42     But it says I am off by 10%.What am I doing wrong?!?!
(a) Determine the object position for which theresulting image is upright andsix times the size of the object.

Your answer is within 10% of the correctvalue. This may be due to roundoff error, or you could have amistake in your calculation. Carry out all intermediate results toat least four-digit accuracy to minimize roundoff error.cm
The problem states that it is wrong, but I don't understandwhy. Here is what I did 1/p + 1/q = 2/R R= 8.2cm Bc resulting image is upright and six timesthe size of the object.     * q= -6p Thus 1/p + 1/ (-6p) = 2/R    5/6p = 2/R    5/6p= 2/8.2cm    p = 3.42     But it says I am off by 10%.What am I doing wrong?!?!

Explanation / Answer

Given :                Raius of curvature (R) = 8.2 cm                     Focal length (f) = R / 2 = 8.2 / 2   = 4.1 cm                Magnification (M) = - v / u   = 6                   ==>   v   = - 6 u We know that :                       1 / f     = 1 / u  +   1/ v         ==>       1 / 4.1 =  1 / u - 1 / 6 u         ==>       0.2439 = 1 / u [ ( 1 - 1/6) ]         ==>      0.2439   = ( 1 / u )* (0.8334)         ==>      0.2439   =   0.8334 / u        or            u           =  0.8334 / 0.2439                                    =   3.4169   cm Hope this helps u!

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