A diminished image of an object is to be obtained on a screen 1.0 m from it. This can be achieved by appropriately placing

Options

A. a concave mirror of suitable focal length
B. a convex mirror of suitable focal length
C. a convex lens of focal length less than 0.25m
D. a concave lens of suitable focal length.

Answer

c.

Explanation

A convex mirror and a concave lens always produce semi image for the object. Therefore, option (b) and (d) are not correct. The image by a convex lens is diminshed when the object is placed beyond 2f.
Let `u=2f+x`.
Using `(1)/(v)-(1)/(u)=(1)/(f)`,
`rArr (1)/(v)-(1)/(-(2f+x))=(1)/(f)rArr (1)/(v)=(1)/(f)-(1)/(2f+x)`
`=(2f+x-f)/(f(2f+x))=((f+x))/(f(2f+x))`
But `u=v=1` (given) `(2f+x)+(f(2f+x))/(f=x)le1`
`rArr 2f=x[1+(f)/(f+x)]le1rArr((2f+x)^(2))/(f+x)le1`
`rArr (2f+x)^(2)lef+x`
The above is true for `flt0.25m`
(c) is the correct answer.