Two lenses of power `-15D` and `+5 D` are in contact with each other. The focal length of the combination is

Options

A. `-20 cm`
B. `-10 cm`
C. `+20 cm`
D. `+10 cm`

Explanation

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

### Step 1: Identify the Powers of the Lenses
Given:
- Power of lens 1 (P1) = -15 D (Diopters)
- Power of lens 2 (P2) = +5 D

### Step 2: Calculate the Total Power of the Combination
The total power (P) of two lenses in contact is given by the formula:
\[ P = P_1 + P_2 \]

Substituting the values:
\[ P = -15 D + 5 D \]
\[ P = -10 D \]

### Step 3: Calculate the Focal Length of the Combination
The focal length (F) of a lens is related to its power (P) by the formula:
\[ F = \frac{1}{P} \]

Substituting the total power:
\[ F = \frac{1}{-10 D} \]

### Step 4: Convert Focal Length to Meters
Calculating the focal length:
\[ F = -0.1 \text{ meters} \]

### Step 5: Convert Focal Length to Centimeters
To convert meters to centimeters:
\[ F = -0.1 \text{ meters} \times 100 \text{ cm/m} = -10 \text{ cm} \]

### Conclusion
The focal length of the combination of the two lenses is:
\[ F = -10 \text{ cm} \]

### Final Answer
The focal length of the combination is -10 cm.

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