$3.)$ An object $10$ mm tall is placed $12$ cm in front of a convex spherical mirror whose radius of curvature is $20$ cm $.$

$($a$.)$ Determine the position, size and orientation of the image.

$($b$.)$ Draw the corresponding ray diagram.

$($c$.)$ Repeat parts $($a$.)$ and $($b$.)$ if the convex mirror is replaced by a concave one.

$4.)$ An object is placed $30$ cm in front of a lens. An upright image is created three times smaller than the object.

$($a$.)$ Calculate the focal length of the lens. Is it converging or diverging?

$($b$.)$ Draw the corresponding ray diagram.

$($c$.)$ Repeat parts $($a$.)$ and $($b$.)$ if the image is inverted and three times smaller than the object.

$5.)$ Two slits spaced $0\mathrm{.}130$ mm apart are placed $90$ cm from a screen and illuminated by coherent light of wavelength $550.$

$($a$.)$ What is the distance in millimeters on the screen between the center of the central maximum and the center of the third$-$order maximum?

$($b$.)$ What is the distance in millimeters on the screen between the center of the central maximum and the first dark fringe?