Question

Find the focal length of the planoconvex polystyrene plastic lens in FIGURE $\mathrm{EX}34.26$.

Short answer

The focal length of the planoconvex polystyrene plastic lens is$68\mathrm{cm}$.

Step-by-step solution

Figure for foal 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

The lens-makers' equation gives the inverse of the focal length $\mathrm{f}$of a narrow lens surrounded by air.

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

Assuming the object is on the left, the lens's initial surface is planar, and we can think of it as a part of a sphere with.

${\mathrm{R}}_1\to \infty$

With${\mathrm{R}}_2=-40$, the second surface behaves as a concave surface.

Focal length 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:

$\frac{1}{\mathrm{f}}=(1.59-1)\left(\frac{1}{\infty \mathrm{cm}}-\frac{1}{-40\mathrm{cm}}\right)$

$\frac{1}{\mathrm{f}}=\frac{59}{4000\mathrm{cm}}$

$\mathrm{f}=\frac{4000}{59}\mathrm{cm}=68\mathrm{cm}$