Question

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.

Answer 1

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.