A convex lens of focal length 50 cm, a concave lens of focal length 50 cm and a concave lens focal lens 20 cm are placed in contact. The power of this combination in diopters will be

Options

A. `-4.67D`
B. `-5D`
C. `-3.21D`
D. `-3D`

Explanation

To find the power of the combination of three lenses placed in contact, we can follow these steps:

### Step 1: Identify the focal lengths of the lenses
- Convex lens (f1) = +50 cm
- Concave lens (f2) = -50 cm (negative because it is concave)
- Concave lens (f3) = -20 cm (negative because it is concave)

### Step 2: Convert the focal lengths to meters
Since power (P) is calculated in diopters (D), we need to convert the focal lengths from centimeters to meters. However, we can directly use the focal lengths in centimeters for the power formula, which is given by:
\[ P = \frac{100}{f} \]
where \( f \) is in centimeters.

### Step 3: Calculate the power of each lens
Using the formula \( P = \frac{100}{f} \):

1. For the convex lens (f1):
\[ P_1 = \frac{100}{50} = 2 \text{ D} \]

2. For the concave lens (f2):
\[ P_2 = \frac{100}{-50} = -2 \text{ D} \]

3. For the concave lens (f3):
\[ P_3 = \frac{100}{-20} = -5 \text{ D} \]

### Step 4: Calculate the total power of the combination
The total power of the combination of lenses is the sum of the individual powers:
\[ P_{total} = P_1 + P_2 + P_3 \]
Substituting the values:
\[ P_{total} = 2 + (-2) + (-5) = 2 - 2 - 5 = -5 \text{ D} \]

### Conclusion
The power of the combination of the three lenses is **-5 diopters**.

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