Question

An object is placed 10 cm in front of a diverging mirror. What is the focal length of the mirror if the image appears 2 cm behind the mirror?

Answer 1

the focal length of the mirror is :
`f=-2.5\,\,cm`

Step-by-step 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:

`(1)/(s) +(1)/(s')=(1)/(f)\\(1)/(10) +(1)/(-2)=(1)/(f)\\(1)/(10) -(1)/(2)=(1)/(f)\\(10\,f)/(10) -(10\,f)/(2)=(10\,f)/(f)\\f-5\,f=10\\-4\,f=10\\f=-2.5\,\,cm`