Question

Two lens of power $-3\mathrm{D}$ and $+2.5\mathrm{D}$ are placed in contact. Find the total power of combination of Lens. Calculate the focal length of this combination.

Answer 1

Step 1: Given data

Power of two lenses

$$\begin{gathered} {\mathrm{P}}_1=-3\mathrm{D} \\ {\mathrm{P}}_2=+2.5\mathrm{D} \end{gathered}$$

Here $\mathrm{D}$ denotes dioptre, unit of power of the lens.

Let the focal length be $\left(\mathrm{F}\right)$.

Step 2: Calculating the power of the combination of lenses and focal length of this combination:

The power of the combination is given by $\left(\mathrm{P}={\mathrm{P}}_1+{\mathrm{P}}_2\right)$

$$\begin{gathered} \mathrm{P}=\left(-3\mathrm{D}\right)+(+2.5\mathrm{D}) \\ \mathrm{P}=-0.5\mathrm{D} \end{gathered}$$

Step 3: Calculate the focal length.

$\begin{array}{rcl}\mathrm{P}& =& \frac{1}{\mathrm{F}(\mathrm{in}m)}\\ \mathrm{F}& =& \frac{1}{\mathrm{P}}\\ \mathrm{F}& =& \frac{1}{\left(-0.5\right)}\\ \mathrm{F}& =& -2m\end{array}$

Hence, the total power of the combination of lens is $-0.5\mathrm{D}$ and the focal length of this combination is $-2m$.