Question

Real and inverted image of an object is formed at a distance $d=40cm$ from the object. The size of the image is half of that of object

Answer 1

Given: v-u=40
magnification=$\frac{1}{2}$
image is real and inverted.
(A) Since the image formed is real image so the nature of lens to be used is converging lens i.e convex lens.
(B) Focal length of lens = f
now magnification=$\frac{-v}{u}=\frac{1}{2}$
Hence, v=$\frac{-u}{2}$
and v-u=40
u=$\frac{-80}{3}$ cm
v=$\frac{40}{3}$ cm
and from lens formula
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\frac{3}{40}+\frac{3}{80}=\frac{1}{f}$
Hence f=$\frac{80}{9}$ cm
(C) From (B) only u=$\frac{80}{3}$ cm
(D) If a mirror is used then. magnifaction = $\frac{v}{u}=\frac{1}{2}$
then v=$\frac{u}{2}$
and v-u=40
$\frac{-u}{2}$=40
u= -80 cm
and v= -40 cm
Since both v and u are negative which means they will be on left side of mirror which is only possible in case of concave mirror.