Two lenses of power 15D and -3D are placed in contact. The focal length of the combination is a

Options

A. 10cm
B. 15cm
C. 12cm
D. 8.33cm

Explanation

To find the focal length of the combination of two lenses with given powers, we can follow these steps:

### Step 1: Identify the Powers of the Lenses
We have two lenses:
- Lens 1 (Convex): Power \( P_1 = 15 \, D \)
- Lens 2 (Concave): Power \( P_2 = -3 \, D \)

### Step 2: Calculate the Equivalent Power of the Combination
The equivalent power \( P \) of two lenses in contact is given by the sum of their individual powers:
\[ P = P_1 + P_2 \]
Substituting the values:
\[ P = 15 \, D + (-3 \, D) = 15 \, D - 3 \, D = 12 \, D \]

### 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:
\[ P = \frac{1}{F} \]
Thus, we can find the focal length \( F \) of the combination:
\[ F = \frac{1}{P} = \frac{1}{12 \, D} \]
Since power in diopters is the reciprocal of the focal length in meters, we have:
\[ F = \frac{1}{12} \, \text{meters} \]

### Step 4: Convert Focal Length to Centimeters
To convert the focal length from meters to centimeters, we multiply by 100:
\[ F = \frac{1}{12} \times 100 = \frac{100}{12} \, \text{cm} = \frac{25}{3} \, \text{cm} \]

### Step 5: Calculate the Decimal Value
Calculating \( \frac{25}{3} \):
\[ \frac{25}{3} \approx 8.33 \, \text{cm} \]

### Final Answer
The focal length of the combination is approximately \( 8.33 \, \text{cm} \).