Question

Find the focal length of the glass lens in FIGURE$\mathrm{EX}34.27$.

Short answer

The focal length of glass lens is$-40\mathrm{cm}$.

Step-by-step solution

Figure for focal length of lens

Figure is,

For surfaces convex toward the object, the radius of curvature$\mathrm{R}$is positive.

For surfaces that are concave toward the object, the radius of curvature $\mathrm{R}$is negative.

Calculation of focal length of lens

Substitute numerical values:If the object is on the left, the lens's initial surface is planar, which we can think of as a part of a sphere with ,$\mathrm{R}=-40\mathrm{cm}$

Withlocalid="1649147855071" $\mathrm{R}=40\mathrm{cm}$, the second surface serves as a concave surface.

The focal length of the lens is ,

$\frac{1}{\mathrm{f}}=(\mathrm{n}-1)\left(\frac{1}{{\mathrm{R}}_1}-\frac{1}{{\mathrm{R}}_2}\right)$

Substitute the following numerical values:

$\frac{1}{\mathrm{f}}=(1.50-1)\left(\frac{1}{-40\mathrm{cm}}-\frac{1}{+40\mathrm{cm}}\right)$

$\frac{1}{\mathrm{f}}=-\frac{1}{40\mathrm{cm}}$$\mathrm{R}=-40\mathrm{cm}$

$\mathrm{f}=-40\mathrm{cm}$