Resnick & Halliday Solutions for Chapter: Images, Exercise 1: Problems

In the given spherical mirrors, object $O$ stands on the central axis of a spherical mirror. For this situation, each problem in the table below gives object distance $p_{\mathrm{s}}$ ($\mathrm{centimeters}$), the type of mirror and then, the distance ($\mathrm{centimeters}$, without proper sign) between the focal point and the mirror. Find $\left(\mathrm{a}\right)$ the radius of curvature $r$ (including sign), $\left(\mathrm{b}\right)$ the image distance $i,$ $\left(\mathrm{c}\right)$ and  the lateral magnification $m.$ Also, determine whether the image is $\left(\mathrm{d}\right)$ real $\left(\mathrm{R}\right)$ or virtual $\left(\mathrm{V}\right)$, $\left(\mathrm{e}\right)$ inverted $\left(\mathrm{I}\right)$ from object $O$ or non-inverted $\left(\mathrm{NI}\right)$ and $\left(\mathrm{f}\right)$ on the same side of the mirror as $O$ or on the opposite side.

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.

Spherical refracting surfaces are given. An object $O$ stands on the central axis of a spherical refracting surface. For this situation, each problem in Table refers to the index of refraction $n_1$ where the object is located, $\left(\mathrm{a}\right)$ the index of refraction $n_2$ on the other side of the refracting surface, $\left(\mathrm{b}\right)$ the object distance $p, \left(\mathrm{c}\right)$ the radius of curvature $r$ of the surface, and $\left(\mathrm{d}\right)$ the image distance $i.$ (All distances are in $\mathrm{centimeters}$) Fill in the missing information, including whether the image is $\left(\mathrm{c}\right)$ real $\left(\mathrm{R}\right)$ or virtual $\left(\mathrm{V}\right)$ and $\left(\mathrm{f}\right)$ on the same side of the surface as object $O$ or on the opposite side.

Two-lens systems. In the figure, stick figure $O$ (the object) stands on the common central axis of two thin, symmetric lenses, which are mounted in the boxed regions. Lens $1$ is mounted within the boxed region closer to $O,$ which is at object distance $p_1.$ Lens $2$ is mounted within the farther boxed region, at distance $d$. Each problem in Table refers to a different combination of lenses and different values for distances, which are given in $\mathrm{centimeters}$. The type of lens is indicated by $C$ for converging and $D$ for diverging; the number after $C$ or $D$ is the distance between a lens and either of its focal points (the proper sign of the focal distance is not indicated).

Find $\left(\mathrm{a}\right)$ the image distance $i_2$ for the image produced by lens $2$ (the final image produced by the system) and $\left(\mathrm{b}\right)$ the overall lateral magnification $M$ for the system, including signs. Also, determine whether the final image is $\left(\mathrm{c}\right)$ real $\left(\mathrm{R}\right)$ or virtual $\left(\mathrm{V}\right)$, $\left(\mathrm{d}\right)$ inverted $\left(I\right)$ from object $O$ or non-inverted $\left(\mathrm{NI}\right)$, and $\left(\mathrm{e}\right)$ on the same side of lens $2$ as the object $O$ or on the opposite side.

Lenses with given radii. Object $O$ stands in front of a thin lens, on the central axis. For this situation, each problem in the table gives object distance $p,$ index of refraction $n$ of the lens, radius $r_1$ of the nearer lens surface, and radius $r_2$ of the farther lens surface. (All distances are in centimetres.) Find (a) the image distance $i$ and (b) the lateral magnification $m$ of the object, including signs. Also, determine whether the image is (c) real ($\mathrm{R}$) or virtual ($\mathrm{V}$), (d) inverted (I) from object $O$ or noninverted ($\mathrm{NI}$), and (e) on the same side of the lens as object $O$ or on the opposite side.

Thin lenses Object $O$ stands on the central axis of a thin symmetric lens. For this situation, each problem in the table gives object distance $p$ (centimetres), the type of lens ($C$) stands for converging and ($D$) for diverging, and then the distance (centimetres, without proper sign) between a focal point and the lens. Find (a) the image distance $i$ and (b) the lateral magnification $m$ of the object, including signs. Also, determine whether the image is (c) real ($\mathrm{R}$) or virtual ($\mathrm{V}$), (d) inverted $\left(\mathrm{I}\right)$ from object $O$ or noninverted $\left(NI\right),$ and (e) on the same side of the lens as object $O$ or on the opposite side.

An object is placed against the center of a thin lens and then moved $60 \mathrm{cm}$ from it along the central axis as the image distance $i$ is measured. The figure gives $i$ versus object distance $p$ out to $p_{\mathrm{s}}=40 \mathrm{cm}.$ What is the image distance when $p=60 \mathrm{cm}?$

A concave shaving mirror has a radius of curvature of $35.0 \mathrm{cm}.$ It is positioned so that the (upright) image of a man's face is $1.70$ times the size of the face. How far is the mirror from the face?