Object Must Be Placed at 15cm from Convex Mirror for Half Size Image

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A virtual image is formed by a convex mirror that has a 30cm focal length. Where must the object be placed if the image is to be half the size of the object?



I know that since the mirror is convex F is negative (F is the focal length). Useful equations are 1/Do + 1/Di = 1/F, where Do is the objects distance and Di is the images distance. I/O = Di/Do, where I is the height of the image and O is the height of the object. And O/I = F/F-Di.



I'm not really sure on where to start could some one give me some pointers.

I = Ox(1/2) or 2I = O

F= -30cm

 

[variation]

Hello,

The amplification I/O also equls to $$\frac{|D_i|}{|D_o|}$$ when we talk about near-axis light.
Be careful and recall that the image is a virtual one and therefore $$D_i$$ is a negative value in Gauss' formula.


Best regards

 

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Thanks for the tip :D