Question

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?

Answer 1

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.