An object of height `h` is held before a spherical mirror of focal length `| f | = 40 cm`. The image of the object produced by the mirror has same orientation as the object and has `height = 0.2 h`. Is the image real or virtual ? Is the image on the convex or concave? What is focal length of mirror with proper sign?

Explanation

We cannot tell the type of mirror form the type of image because bothtypes of mirror can produce virtual images. Similarly, we cannot tell the type of mirror from the sign of the focal length f, as obtained from Eq. 34-3 or Eq. 34-4, because we lack enough information to use either equation. However, we can make use of the magnification information.
Calculations : From the given information, we know that the ratio of image height h. to object height h is 0.20. Thus from Eq. 34-5 we have
`|m| =(h_(i))/(h_(0)) = 0.20`
Because the object and image have the same orientation, we know that m must be positive m = + 0.20. Substituting this into Eq. 34-6 and solving for say,i gives us
`v = - 0.20 u`,
which does not appear to be of help in finding f. However, it is helpful if we substitute it into Eq. 34-4.That equation gives us
`(1)/(f) = (1)/(i) + (1)/(p) = (1)/(-0.20p) + (1)/(p = (1)/(p) (-5 + 1)`
from which we find
`f = -p/4`.
Now we have it : Because p is positive, f must be negative, which means that the mirror is convex with `f = -40 cm`.