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10pm.

"Show mathematically that to produce an image that is the same size as the object in a concave mirror, the object needs to be at twice the focal length from the mirror."

"1/o + 1/o=1/f
1/2f + 1/i=1/f
1/i=1/2f
i=2f

M=di/do= 2f/2f= 1

check my thinking."

could someone please explain, I'm not really following.

the mirror equation
1/do+ 1/di= 1/f I assume you are familiar with that. I see I had a typo in the first line.

multiply by do
do/do+do/di= do/f
1+ M=do/f
but M (do/di=ho/hi= 1 given)
1+1=do/f which means that do is twice f.

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