A concave mirror magnifies an object placed 30.0cm from the mirror by a factor of +3.0. Calculate the radius of curvature of the mirror. Please, if possible include a step by step method. Thank you!

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Let's apply the mirror equation which is:

`1/d_o + 1/d_i=1/f`


where `d_o` ` `- object distance, `d_i` ` `-  image distance and `f ` - focal length.

Note that, magnification factor is the ratio of image distance to object distance.

Magnification factor `= ` `-d_i/d_o`


Since magnification factor is +3 and object distance is 30 cm, then


` `

Isolate `d_i` .


` `

Then, substitute `d_o=30` cm and `d_i=-90`  cm  to the mirror equation.

`1/30 + 1/(-90)=1/f`

` `

To simplify the equation, multiply both sides by the LCD which is 90f.

`90f*(1/30 + 1/(-90))=(1/f) *90f`



Solve for f.


`f=45` cm

Moreover in curved mirrors,  the focal length is half the raduis of the curvature of mirror. So,

`f = R/2`

Substitute value of f.


Isolate R.

`45*2 = R`


Hence, the raduis of curvature of the mirror is 90 cm.

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