A convex lens and a concave lens, each having same focal length of `25 cm`, are put in contact to form a combination of lenses. The power in diopters of the combination is

Options

A. 25
B. 50
C. infinite
D. zero

Explanation

To solve the problem of finding the power of a combination of a convex lens and a concave lens, both with the same focal length of 25 cm, we can follow these steps:

### Step 1: Identify the Focal Lengths
- The focal length of the convex lens (F1) is +25 cm (positive because it converges light).
- The focal length of the concave lens (F2) is -25 cm (negative because it diverges light).

### Step 2: Convert Focal Lengths to Power
The power (P) of a lens is given by the formula:
\[ P = \frac{100}{F} \]
where F is the focal length in centimeters.

- For the convex lens:
\[ P_1 = \frac{100}{F_1} = \frac{100}{25} = +4 \text{ diopters} \]

- For the concave lens:
\[ P_2 = \frac{100}{F_2} = \frac{100}{-25} = -4 \text{ diopters} \]

### Step 3: Calculate the Total Power of the Combination
When two lenses are in contact, the total power (P) of the combination is the sum of the individual powers:
\[ P = P_1 + P_2 \]

Substituting the values we found:
\[ P = +4 + (-4) = 0 \text{ diopters} \]

### Conclusion
The power of the combination of the convex lens and the concave lens is **0 diopters**.

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