Figure $($a$)$ shows the basic structure of a camera. A lens can be moved forward or back to produce an image on film at the back of the camera. For a certain camera, with the distance i between the lens and the film set at $f=5\mathrm{.}75cm,$ parallel light rays from a very distant object O converge to a point image on the film, as shown. The object is now brought closer, to a distance of $p=214cm,$ and the lensfilm distance is adjusted so that an inverted real image forms on the film $($Figure $($b$)).($a$)$ What is the lens$-$film distance inow $($in cm$)?($b$)$ By how much $($in cm $)$ was distance i changed?

$($a$)$ Number

Units

$($b$)$ Number

Units