Two thin lenses of power $+2.0D$ and $-1.5D$ are placed in contact. Find the a. power and b. focal length of the combination of lenses. c. Also state the nature of the lens formed by the combination of these lenses.

Step 1 - Given data.

Let the power of lens 1 be $P_1=+2.0D$.
Let the power of lens 2 be $P_2=-1.5D$.

Step 2 - Formula Used.
The formula for calculating the total power is $P=P_1+P_2$.
The focal length $\left(f\right)$ of the combination of lenses can be found using the formula for power which is given as: $P=\frac{1}{f}$. Therefore, $f=\frac{1}{P}$.

Step 3 - Finding the total power.

Substitute the values into the formula to calculate the total power.

$$\begin{gathered} P=P_1+P_2 \\ P=+2.0-1.5 \\ P=0.5D \end{gathered}$$

Step 4 - Finding the focal length of the combination of lenses.

Substitute the values into the formula for power to calculate the focal length of the combination of lenses.

$$\begin{gathered} f=\frac{1}{P} \\ f=\frac{1}{0.5D} \\ f=2m \\ f=+200cm \end{gathered}$$

(Note:- $m^{-1}=D$ and$1m=100cm$)

Since the focal length of the combination of lenses is positive, the two lenses together act as a converging(convex) lens.

a. The total power is $0.5D$.
b. The focal length of the combination of the lenses is $+200cm$.
c. The two lenses together act as a converging(convex) lens.