Question

find the distance of the image when an object is placed on the principal Axis at a distance of 10 cm in front of a concave mirror whose radius of curvature is 8

Answer 1

The mirror formula:
1/f = 1/u + 1/v
where u = the distance of the object from the pole and v = the distance of the image from the pole
u = -10 cm (to the left of the mirror)
Since, 2f = r
f = r/2
Therefore, f = 4 cm
v will be negative as the image will be in the left of the mirror.
The formula after substitution of the values:
1/4 = -1/10 + -1/v
-> -1/v = 1/4 + 1/10
-> -1/v = 5/20 + 2/20
-> -1/v = 7/20
-> -v = 20/7
-> v = -20/7 cm
Thus, the distance of the image from the mirror is 20/7 or 2 6/7 cm.

u and v were negative because according to the number line, the numbers towards the left of 0 (pole) are negative.