Two lenses have focal lengths `f_(1)` and `f_(2)` and their dispersive powers are `omega_(1)` and `omega_(2)` respectively. They will together form an achromatic combination if

Options

A. `omega_(1)f_(1) = omega_(2)f_(2)`
B. `omega_(1)f_(2) + omega_(2)f_(1) = 0`
C. `omega_(1)+f_(1) = omega_(2)+f_(2)`
D. `omega_(1)-f_(1) = omega_(2)-f_(2)`

Explanation

To determine the condition for two lenses to form an achromatic combination, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept**:
- An achromatic combination of lenses is one where the combination does not disperse light into its constituent colors. This is achieved when the chromatic aberration introduced by the two lenses cancels each other out.

2. **Using the Formula**:
- The condition for two lenses to form an achromatic combination can be expressed mathematically. The formula is:
\[ \frac{\omega_1}{f_1} + \frac{\omega_2}{f_2} = 0 \]
where \( \omega_1 \) and \( \omega_2 \) are the dispersive powers of the two lenses, and \( f_1 \) and \( f_2 \) are their respective focal lengths.

3. **Cross-Multiplying**:
- Rearranging the formula gives:
\[ \omega_1 f_2 + \omega_2 f_1 = 0 \]
This indicates that the sum of the products of the dispersive power and focal lengths must equal zero.

4. **Identifying the Correct Option**:
- Now, we will check the provided options against our derived equation:
- Option 1: \( \omega_1 f_1 = \omega_2 f_2 \) (not correct)
- Option 2: \( \omega_1 f_2 + \omega_2 f_1 = 0 \) (correct)
- Option 3: \( \omega_1 + f_1 = \omega_2 + f_2 \) (not correct)
- Option 4: \( \omega_1 - f_1 = \omega_2 - f_2 \) (not correct)

5. **Conclusion**:
- The correct condition for the two lenses to form an achromatic combination is given by:
\[ \omega_1 f_2 + \omega_2 f_1 = 0 \]
Therefore, the answer is **Option 2**.