Question

Find the size, position and nature of image formed when an object of size 1cm is placed at a distance of 15cm from a concave mirror of focal length 10cm.

Answer 1

the size of the image will be double the size of the object i.e. m=2, image distance=-30, the image will be inverted, real and magnified

Answer 2

The formula to find that is $\displaystyle{i}=\frac{1}{{{\left(\frac{1}{{f}}\right)}-{\left(\frac{1}{{o}}\right)}}}$ where o is the distance of the object and f is the focal length, and i is the image distance, we know that the mirror is concave and the distance is greater than the focal length of the mirror, so we know the rays intersect on our side of the mirror, that means the image is real and flipped upside down. 
The magnitud equation is $M= - \frac{i}{o} = \frac{hi}{ho}$ where hi and ho means height of image and object respectively.
Evaluating we find that i is 30 cm, that means double the distance of the object, so M is -2 therefore ho must be -0.5 cm the object is upside down and it looks half the size of the original object.