Use the mirror equation to deduce that
a. An object placed between f and 2f of a concave mirror produces a real image beyond 2f.

Explanation

a. `(1)/(u) + (1)/(v) = (1)/(f) , (1)/(V) = (1)/(f) - (1)/(u) `............... (1)
f and u are negative . i.e, f `lt` 0 and `u lt 0` .
Object is placed between f and 2f, then
`2f lt u lt f or (1)/(2f) gt (1)/(u) gt (1)/(f) `
i.e., - `(1)/(2f) lt - (1)/(u) lt - (1)/(f) `
`(1)/(f) - (1)/(2f) lt (1)/(f) - (1)/(u) lt (1)/(f) - (1)/(f) `
Using equation (1) `rArr (1)/(2f) lt (1)/(v) lt 0 `
i.e., .v. is negative, the image formed is real and beyond 2f.