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?

The figure gives the lateral magnification $m$ of an object versus the object distance $p$ from a lens, as the object is moved along the central axis of the lens through a range of values for $p$ out to $p_{\mathrm{s}}=20.0 \mathrm{cm}.$ What is the magnification of the object when the object is $38 \mathrm{cm}$ from the lens?

Object $O$ stands on the central axis of a thin symmetric lens. For this situation, each problem in table refers to $\left(\mathrm{a}\right)$ the lens type, converging $\left(C\right)$ or diverging $\left(D\right), \left(\mathrm{b}\right)$ the focal distance $f.$ $\left(\mathrm{c}\right)$ the object distance $p,$ $\left(\mathrm{d}\right)$ the image distance $i,$ and $\left(\mathrm{e}\right)$ the lateral magnification $m.$ (All distances are in $\mathrm{centimeters}$) It also refers to whether $\left(\mathrm{f}\right)$ the image is real $\left(\mathrm{R}\right)$ or virtual $\left(\mathrm{V}\right), \left(\mathrm{g}\right)$inverted $\left(\mathrm{I}\right)$ or non-inverted $\left(\mathrm{NI}\right)$ from $O,$ and $\left(\mathrm{h}\right)$ on the same side of the lens as $O$ or on the opposite side. Fill in the missing information, including the value of $m$ when only inequality is given. Where only a sign is missing, answer with the sign.

The figure gives the lateral magnification $m$ of an object versus the object distance $p$ from a spherical mirror, as the object is moved along the mirror's central axis through a range of values for $p$. The horizontal scale is set by $p_{\mathrm{s}}=10.0 \mathrm{cm}$. What is the magnification of the object when the object is $24 \mathrm{cm}$ from the mirror?

In the figure, an isotropic point source of tight $S$ is positioned at distance $d$ from a viewing screen $A$ and the light intensity $I_{\mathrm{P}}$ at point $P$ (level with $S$) is measured. Then a plane mirror $M$ is placed behind $S$ at distance $D$. By how much is $I_{\mathrm{P}}$ multiplied by the presence of the mirror, if $D=2d$?

The figure a shows the basic structure of an old film camera. A lens can be moved forward or back to produce an image on film at the back of the camera. For a certain camera, with the distance $i$ between the lens and the film set at $f=5.0 \mathrm{cm},$ parallel light rays from a very distant object $O$ converge to a point image on the film, as shown. The object is now brought closer, to a distance of $p=120 \mathrm{cm},$ and the lens-film distance is adjusted so that an inverted real image forms on the film figure $\left(b\right)$. $\left(\mathrm{a}\right)$ What is the lens-film distance $i$ now? (b) By how much was distance $i$ changed?

$\left(\mathrm{a}\right)$  

$\left(\mathrm{b}\right)$ 

In the figure, a beam of parallel light rays from a laser is incident on a solid transparent sphere of index of refraction $n$. (a) If a point image is produced at the back of the sphere, what is the index of refraction of the sphere? (b) What index of refraction, if any, will produce a point image at the center of the sphere?