An object 5 cm high is placed at a distance 60 cm in front of a concave mirror of focal length 10 cm. Find the position and size of the image by drawing.

To solve this problem, we will use the mirror formula and the magnification formula.

1. The mirror formula is 1/f = 1/v + 1/u. Here, f is the focal length of the mirror, v is the image distance, and u is the object distance.

2. Given in the problem, the object distance u = -60 cm (the negative sign indicates that the object is on the same side as the light being reflected), and the focal length f = -10 cm (the negative sign indicates a concave mirror).

3. Substituting these values into the mirror formula, we get 1/-10 = 1/v - 1/-60.

4. Solving this equation for v, we get v = -15 cm. The negative sign indicates that the image is formed on the same side as the light being reflected, which is the case for a real image formed by a concave mirror.

5. The magnification formula is m = -v/u = h'/h. Here, m is the magnification, h' is the height of the image, and h is the height of the object.

6. Given in the problem, the object height h = 5 cm. Substituting the known values into the magnification formula, we get -(-15)/-60 = h'/5.

7. Solving this equation for h', we get h' = -1.25 cm. The negative sign indicates that the image is inverted.

So, the image is formed 15 cm in front of the mirror, and it is 1.25 cm high and inverted.

As for the drawing, it's a bit difficult to illustrate here, but you would draw a concave mirror with the object 60 cm in front of it and the image 15 cm in front of it, inverted.