50 through 57 55, 57 53 Thin lenses. Object $\mathbf{O}$stands on the central axis of a thin symmetric lens. For this situation, each problem in Table 34-6 gives object distance p (centimeters), the type of lens (C stands for converging and D for diverging), and then the distance (centimeters, without proper sign) between a focal point and the lens. Find (a) the image distance $\mathbf{i}$ and (b) the lateral magnification m of the object, including signs. Also, determine whether the image is (c) real $\left(R\right)$ or virtual $\left(V\right)$ , (d) inverted $\left(I\right)$ from object $\mathbf{O}$ or non inverted $\left(\mathrm{NI}\right)$, and (e) on the same side of the lens as object $\mathbf{O}$or on the opposite side.

The lens is diverging

Focal length,$\mathrm{f}=-12.0\mathrm{cm}$

Object distance, $\mathrm{p}=+8$

By using the thin lens equation and the formula for magnification, we can find all the required quantities.

Formula:

Thin lens equation,$\frac{1}{\mathrm{f}}=\frac{1}{\mathrm{p}}+\frac{1}{\mathrm{i}}$

Magnification,$\mathrm{m}=-\frac{\mathrm{i}}{\mathrm{p}}$

Since the lens is diverging, the focal length value should be negative, i.e.

$\mathrm{f}=-12\mathrm{cm}$

Thin lens equation is

$\begin{array}{c}\frac{1}{\mathrm{f}}=\frac{1}{\mathrm{p}}+\frac{1}{\mathrm{i}}\\ \frac{1}{(-12)}=\frac{1}{8}+\frac{1}{\mathrm{i}}\\ \frac{1}{\mathrm{i}}=\frac{1}{(-12)}-\frac{1}{8}\\ \frac{1}{\mathrm{i}}=-0.2083\end{array}$

$\mathrm{i}=-4.8\mathrm{cm}$

Image distance $\mathrm{i}=-4.8\mathrm{cm}$

Magnification is,

$\begin{array}{c}\mathrm{m}=-\frac{\mathrm{i}}{\mathrm{p}}\\ =-\left(\frac{-4.8}{8}\right)\\ =+0.60\end{array}$

Lateral magnification $\mathrm{m}=+0.60$

As the image distance$\mathrm{i}$ is negative, the image is virtual $\left(\mathrm{V}\right)$.

As the magnification is positive, the image is non-inverted $\left(NI\right)$.

For thin lens, the real images form on the opposite side as the object and virtual images form on the same side as the object.

Since the image is non-inverted, it forms on the same side of the object.