Two lenses of power +12 D and -2 D are combined together. What is their equivalent focal length ?

Options

A. 8.33 cm
B. 10 cm
C. 14 cm
D. 12.5 cm

Answer

To find the equivalent focal length of two combined lenses, we can use the formula relating the power of the lenses to their focal lengths. The power (P) of a lens is given by the formula:

\[ P = \frac{1}{f} \]

where \( f \) is the focal length in meters.

1. **Calculate the individual powers**:
- For the first lens (P1 = +12 D):
\[ P_1 = +12 \, \text{D} \]
- For the second lens (P2 = -2 D):
\[ P_2 = -2 \, \text{D} \]

2. **Find the total power of the combined lenses**:
The total power (P_total) of two lenses in combination is given by:
\[ P_{\text{total}} = P_1 + P_2 \]
Substituting the values:
\[ P_{\text{total}} = 12 \, \text{D} + (-2 \, \text{D}) \]
\[ P_{\text{total}} = 12 - 2 = 10 \, \text{D} \]

3. **Calculate the equivalent focal length**:
Using the power to focal length relationship:
\[ P_{\text{total}} = \frac{1}{f_{\text{eq}}} \]
Rearranging gives:
\[ f_{\text{eq}} = \frac{1}{P_{\text{total}}} \]
Substituting the total power:
\[ f_{\text{eq}} = \frac{1}{10 \, \text{D}} \]
Converting diopters to meters:
\[ f_{\text{eq}} = 0.1 \, \text{m} \]
Converting meters to centimeters:
\[ f_{\text{eq}} = 10 \, \text{cm} \]

Thus, the equivalent focal length of the combined lenses is **10 cm**.