Question

A convex mirror of focal length 32cm produces an image of a book at a distance, do in front of the mirror. Given that the image is half the size of the book, calculate the distance between the book and its image

Answer 1

the distance between the book and its image = 144 cm
that find from the law of magnification. and the general law of mirror

Answer 2

You need to assume that the image is either upright or inverted because it's not stated in your problem. Once you make that assumption, use the formula for magnification and remember that:\[m=\frac{ -i }{ o }\]You should not be able to find a ratio between the image distance, i, and the object distance, o. You should then be able to use the following equation to get an answer:\[\frac{ 1 }{ f }=\frac{ 1 }{ o }+\frac{ 1 }{ i }\].

Remember this: if you assumed the image is real and thus inverted, it will be on the same side of the mirror as the object. This means that both the image distance and the object distance are on the same side of the mirror and beyond the mirror's focal point, which as the problem states is 32cm in front of the mirror. If you decide the image is upright, that means the object distance is between the mirror and its focal point and that the image lies on the other side of the mirror.