A patient can't see objects closer than $38\mathrm{.}3$ cm and wishes to clearly see objects that are $20\mathrm{.}0$ cm from his eye.

$($a$)$ Is the patient nearsighted or farsighted?

nearsighted

farsighted

$($b$)$ If the eye$-$lens distance is $2\mathrm{.}09$ cm $,$ what is the minimum object distance $p$ from the lens? $($Give your answer to at least three significant digits.$)$ cm

$($c$)$ What image position with respect to the lens will allow the patient to see the object? $($Give your answer to at least three significant digits.$)$ cm

$($d$)$ Is the image real or virtual? Is the image distance $q$ positive or negative? $($Select all that apply.$)$

real image

virtual image

distance is positive

distance is negative

$($e$)$ Calculate the required focal length.

$$ cm

$($f$)$ Find the power of the lens in diopters. diopters

$($g$)$ If a contact lens is to be prescribed instead, find $p,q,$ and $f,$ and the power of the lens.