A camera lens is initially set at f$/22$ for a shutter speed of $1/31\mathrm{.}25$ s$.$ If the amount of lighting on the subject is unchanged, and the lens is set at f$/11,$ what is the proper shutter speed at this setting?

a$.$

$1/15$ s

b$.$

$1/125$ s

c$.$

$1/8$ s

d$.$

$1/4$ s

e$.$

$1/22$ s