Two thin lenses having optical powers of -10 D and + 6 D are placed in contact with each other. The focal length of the combination is : 

Options

A. ` + 0-25 cm`
B. `– 0.25 cm`
C. `+ 0.25 m`
D. `-0.25 m`

Explanation

To find the focal length of the combination of two thin lenses placed in contact, we can follow these steps:

### Step 1: Identify the optical powers of the lenses
We have two lenses with the following optical powers:
- Lens 1 (P1) = -10 D (diopters)
- Lens 2 (P2) = +6 D (diopters)

### Step 2: Calculate the total optical power of the combination
When two lenses are placed in contact, the total optical power (P) of the combination is the sum of the individual powers:
\[ P = P_1 + P_2 \]
Substituting the values:
\[ P = -10 D + 6 D = -4 D \]

### Step 3: Calculate the focal length of the combination
The focal length (f) of a lens is related to its optical power (P) by the formula:
\[ f = \frac{1}{P} \]
Substituting the total power we found:
\[ f = \frac{1}{-4 D} = -0.25 \text{ meters} \]

### Conclusion
The focal length of the combination of the two lenses is -0.25 meters.