Answer:
the focal length of the mirror is : [tex]f=-2.5\,\,cm[/tex]
Explanation:
Use the formula for the formation of image using a divergent mirror and recalling that the image (s') that this mirror formed is virtual, so it is entered as a negative number in the formula. Use the object position (s) as 10, the image position (s') as -2, and derive the value of the focal length:
[tex]\frac{1}{s} +\frac{1}{s'}=\frac{1}{f}\\\frac{1}{10} +\frac{1}{-2}=\frac{1}{f}\\\frac{1}{10} -\frac{1}{2}=\frac{1}{f}\\\frac{10\,f}{10} -\frac{10\,f}{2}=\frac{10\,f}{f}\\f-5\,f=10\\-4\,f=10\\f=-2.5\,\,cm[/tex]
