An object is placed 15cm from a mirror and an image is captured on the screen with magnification 2. Calculate the focal length of the mirror and determing if it is concave or convex.

Explanation

Consider the situation shown in the following figure which also indicates the coordiinate system.
Here, `u=-15cm and m=-2`.
Note the negative sign for m. The fact that the image is captured on the screen implies the image is real. Therefore, the agnification is to be taken negative, thought the problem simply states that the magnification is 2.
Substituting in equation
`m =-(v)/(u)` , we get `v=-30 cm `
Substituting in equation
`(1)/(v)+(1)/(u)=(1)/(f)` , we get `f=-10 cm `
conclusion: The focal length of the mirror is 10cm. The negative sign implies it is concave.