In front of a spherical concave mirror of radius 39cm, you position and object of height 0.6cm somewhere along the principal axis. The resultant image has a height of 0.2cm, How far from the mirror is the object located?
What if this were a convex mirror with the same radius, and the same image and object height?
The Attempt at a Solution
1/2R=19.5cm focal point
I have two equations with two unknowns (Di and Do). I used the equation Hi/Ho=-Di/Do to solve the equation for -Di, getting 0.2/0.6= 1/3. 1/3=-Di/Do, solving for Di I get -1/3Do=Di.
I then just plug this equation into the mirror equation
1/do+1/(-1/3do)=1/f..... I bring the -3 from the denominator into the numerator
1/f is 2/39
I follow the same process for a convex mirror but I get a positive answer with the same value of 39. I don't think a negative answer makes sense, and I am unsure of my sign usage... I find it odd that my object distance is the same as my mirrors radius.
Thank you in advance for the help.