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

As the image of the object has the same orientation as the object, the image must be virtual, and on the opposite side of the object.
Now, `m = (h_(2))/(h_(1)) = -(v)/(u) = 0.2`
`:. v = -0.2 u`
From `(1)/(f) = (1)/(v) + (1)/(u)` ,
`(1)/(f) = (1)/(-0.2 u) + (1)/(u) = -(4)/(u)`
`f = -(u)/(4)`. As `u` is negative, `f` must be positive,
i.e., `f = + 40 cm`. The mirror must be convex.