In Figure P$35\mathrm{.}30,$ a thin converging lens of focal length $14\mathrm{.}0$ cm forms an image of the square abcd, which is hc $5$ hb $510\mathrm{.}0$ cm high and lies between distances of pd $520\mathrm{.}0$ cm and pa $530\mathrm{.}0$ cm from the lens. Let a$9,$ b$9,$ c$9,$ and d$9$ represent the respective corners

of the image. Let qa rep$-$

resent the image distance

for points a$9$ and b$9,$ qd

represent the image dis$-$

tanceforpointsc$9$and

d$9,$ h$9$b represent the dis$-$

tance from point b$9$ to the

axis, and hc$9$ represent the

height of c$9.($a$)$ Find qa$,$

qd$,$ h$9$b$,$ and hc$9.($b$)$ Make

a sketch of the image.

$($c$)$ The area of the object is $100$ cm$2.$ By carrying out the following steps, you will evaluate the area of the image. Let q represent the image distance of any point between a$9$ and d$9,$ for which the object distance is p$.$ Let h$9$ represent the dis$-$ tance from the axis to the point at the edge of the image between b$9$ and c$9$ at image distance q$.$ Demonstrate that

$|$h$9|510\mathrm{.}0$q $14\mathrm{.}02$ q