Question

Two thin lenses of power $+3.5D$ and $-2.5D$ are placed in contact. Find the power and focal length of the lens combination.

Answer 1

Step 1 - Given data

Power of the first thin lens $P_1=+3.5D$.

Power of the second thin lens $P_2=-2.5D$

Step 2 - Formula used

The power of a combination of lenses is given by,

$P=P_1+P_2$

Where $P$ is the power of a combination of lenses.

Step 3 - Finding the power of a combination of lenses

Substitute the values into the formula.

$$\begin{gathered} P=3.5D-2.5D \\ =+1D \end{gathered}$$

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

Relation between the focal length and the power of the lens is given by,

$P=\frac{1}{f}$

where $f$ is the focal length of a combination of lenses.

Substitute the value of $P$ into the formula to calculate the focal length.

$$\begin{gathered} +1D=\frac{1}{f} \\ f=\frac{1}{1m^{-1}}\left(D=m^{-1}\right) \\ f=1m \\ f=100cm \end{gathered}$$

1. The power of the lens combination is $+1D$.
2. The focal length of the combination is $100cm$