An object is places 15 cm from a mirror and an erect image of size 5cm is seen. Determing the focal length and the nature of the mirror. Assume the object size is 15 cm.

Explanation

Consider the situation shown in the following figure where the optical element is represented by a box as we do not known its nature.
Here `u=-15cm` ,
` h_(i)=+5cm,` and
`h_(v)=+5cm. `
Substituting in equation
` m=(h_(i))/(h_(0))=+(1)/(3) and m=(-v)/(u),` we get `v=+5 cm `
Subtituting in equation
`(1)/(v)+(1)/(u)=(1)/(f)`, we g e t `f=+75`
Conclusion: The focal length of the mirror is `7.5cm` . The positive sign implies that the mirror is convex.