A $9\mathrm{.}00$ cm $-$high clown was placed $176$ cm away $($caution: diagram might not be to scale$)$ from a glass double convex lens. The focal length of the lens is $\backslash ($ d$\_\{$f$\}=60\mathrm{.}0\backslash$mathrm$\{$~cm$\}\backslash ).$

a$.$ What is the distance separating the position of the formed image from the lens?

$\backslash [$

d$\_\{$i$\}=$

$\backslash ]$

b$.$ What is the height of the image? $($Remember: an upright image is positive and a flipped image is negative$)$

$\backslash [$

h$\_\{$i$\}=$

$\backslash ]$

A $\backslash ($ d$\_\{$f$\}=154\backslash$mathrm$\{$~cm$\}\backslash )$ focal length double convex lens is placed in the other side of the first lens $247$ cm away.

c$.$ Where would this second lens form an image of the clown relative to this second lens?

d$.$ Determine the height, orientation and type of the image formed.

$\backslash [$

h$\_\{$i$\}=$

$\backslash ]$

e$.$ Assuming that the two convex sides of the second lens have the same radius $\backslash ($ R $\backslash ),$ and assuming that the lens' index of refraction is $1\mathrm{.}47,$ find $\backslash ($ R $\backslash ).$

$\backslash [$

R$=$

$\backslash ]$