Question

A 2.0-cm-diameter spider is 2.8 m from a wall. Determine the focal length f and position s′ in meters (measured from the wall) of a lens that will make a half-size image of the spider on the wall.

Answer 1

We know that the equation of lens

1/d_i + 1/d_o = 1/f
where d_i is the distance of image from the lens
d_o is the object distance from the lens.
and f if the focal length of the lens.
Now it is given that image size is (1/2) of the object size.
m = (-d_i/d_o) = I/O
where I is the image size and O is the object size
hence m = -(1/2)
because image must be inverted
(-d_i/d_o) = -(1/2)
d_o = 2d_i
Since image is on the wall , therefore
d_o+d_i = 2.8 -----------(1)
2d_i + d_i = 2.8
3d_i = 2.8
d_i = 2.8/3
and d_o = 2d_i = 5.6/3
Using the values in the lens formula
(3/2.8) + (3/5.6) = 1/f
f = 0.622 m