Why does a camera focus sharpest at 10 m when photographing a mirror image from 5 m away?

[Pranav Jha]

If I wish to take a picture of your image while standing 5 m in front of a
plane mirror, for what distance should I set your camera to provide the
sharpest focus.

I guessed the answer would be 10m (distance of object+distance of image). But i don't know why the focus of camera would be sharpest at that distance?

 

[jtbell]

The light that that enters the camera lens diverges from the image point, exactly as if you removed the mirror and placed the object at that location. The light rays travel exactly the same paths just before they enter the camera, in both cases.

 

[Pranav Jha]

The light that that enters the camera lens diverges from the image point, exactly as if you removed the mirror and placed the object at that location. .

Could you please explain this further

 

[sophiecentaur]

Have a look at this
http://www.physicsclassroom.com/class/refln/u13l2b.cfm"

 

[DaveC426913]

Could you please explain this further

Simply put: a mirror will reflect the rays from an object to the camera; but it does not change the total distance. The total distance from object to camera is 10m, thus the camera wants to focus at 10m.

Draw a picture.