In figure, a real inverted image $l$ of an object $O$ is formed by a particular lens (not shown), the object-image separation is $d=50.0 \mathrm{cm},$ measured along the central axis of the lens. The image is just half the size of the object. $\left(a\right)$ What kind of lens must be used to produce this image? $\left(b\right)$ How far from the object must the lens be placed? $\left(c\right)$ What is the focal length of the lens?

An object is moved along the central axis of a spherical mirror while the lateral magnification $m$ of it is measured. The figure gives $m$ versus object distance $p$ for the range $p_{\mathrm{a}}=2.0 \mathrm{cm}$ to $p_{\mathrm{b}}=8.0 \mathrm{cm}$. What is $m$ for $p=20.0 \mathrm{cm}$?

In the given mirrors object $O$ stands on the central axis of a spherical or plane mirror. For this situation, each problem in the table below refers to $\left(\mathrm{a}\right)$ the type of mirror, $\left(\mathrm{b}\right)$ the focal distance $f, \left(\mathrm{c}\right)$ the radius of curvature $r, \left(\mathrm{d}\right)$ the object distance $p,$ $\left(\mathrm{e}\right)$ the image distance $i$ and $\left(\mathrm{f}\right)$ the lateral magnification $m$. (All distances are in $\mathrm{centimeters}$) It also refers to whether $\left(\mathrm{g}\right)$ the image is real $\left(\mathrm{R}\right)$ or virtual $\left(\mathrm{V}\right)$, $\left(\mathrm{h}\right)$ inverted  $\left(\mathrm{I}\right)$ or non-inverted $\left(\mathrm{NI}\right)$ from $O,$ and $\left(\mathrm{i}\right)$ on the same side of the mirror as object $O$ or on the opposite side. Fill in the missing information. Where only a sign is missing, answer with the sign.$\mathrm{I}$

An object is moved along the central axis of a thin lens while the lateral magnification $m$ is measured. Figure gives $m$ versus object distance $p$, out to $p_{\mathrm{s}}=16.0 \mathrm{cm}$. What is the magnification of the object when the object is $14.0 \mathrm{cm}$ from the lens?

In a microscope of the type shown in the figure, the focal length of the objective is $3.00 \mathrm{cm}$ and that of the eyepiece is $8.00 \mathrm{cm}.$ The distance between the lenses is $25.0 \mathrm{cm}.$ (a) What is the tube length $s$? (b) If image $l$ in the figure is to be just inside focal point $F_1\text{'}$, how far from the objective should the object be? What then are $\left(\mathrm{c}\right)$ the lateral magnification $m$ of the objective.
(d) the angular magnification $m_{\mathrm{\theta }}$ of the eyepiece, and (e) the overall magnification $M$ of the microscope?

In the figure, $r=5.0 \mathrm{cm}$ and index of refraction $1.5.$ A paperweight is constructed by slicing through the sphere along a plane that is $2.0 \mathrm{cm}$ from the center of the sphere, leaving height $h=3.0 \mathrm{cm}.$ The paperweight is placed on a table and viewed from directly above by an observer who is distance $d=10.0 \mathrm{cm}$ from the tabletop (Figure). When viewed through the paperweight, how far away does the tabletop appear to be to the observer?