It is desired to make an achromatic combination of two lenses, `(L_(1)& L_(2))` made of materials having dispersive power `omega_(1)` and `omega_(2)(ltomega_(1))`. If the combination of lenses is converging then:

Options

A. `L_(1)` is converging
B. `L_(2)` is converging
C. Magnitude power of `L_(1)` is greater than the magnitude power of `L_(2)`
D. both lenses should be conversing.

Explanation

To solve the problem of making an achromatic combination of two lenses \( L_1 \) and \( L_2 \) with dispersive powers \( \omega_1 \) and \( \omega_2 \) (where \( \omega_2 < \omega_1 \)), we need to follow these steps:

### Step-by-Step Solution:

1. **Understanding Dispersive Power**:
The dispersive power \( \omega \) of a lens is defined as:
\[ \omega = \frac{n - 1}{n - n'} \]
where \( n \) is the refractive index of the lens material for a specific wavelength, and \( n' \) is the refractive index for another wavelength.

2. **Lenses Combination**:
For two lenses to form an achromatic combination, the condition that must be satisfied is:
\[ \omega_1 P_1 + \omega_2 P_2 = 0 \]
where \( P_1 \) and \( P_2 \) are the powers of lenses \( L_1 \) and \( L_2 \) respectively.

3. **Lens Maker's Formula**:
The power \( P \) of a lens is given by:
\[ P = \frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]
where \( f \) is the focal length and \( R_1, R_2 \) are the radii of curvature of the lens surfaces.

4. **Power Relation**:
Since \( \omega \) is inversely related to the power of the lens, we can say:
\[ P \propto \frac{1}{\omega} \]
This implies that if \( \omega \) is smaller, the power \( P \) is larger.

5. **Condition for Converging Lenses**:
Given that \( \omega_2 < \omega_1 \), it follows that:
\[ P_2 > P_1 \]
Therefore, lens \( L_2 \) must have a greater power than lens \( L_1 \) for the combination to be converging.

6. **Conclusion**:
Since the combination of lenses is converging, we conclude that:
\[ \text{Power of } L_2 > \text{Power of } L_1 \]
Thus, \( \omega_2 < \omega_1 \) indicates that \( L_2 \) is the converging lens.

### Final Answer:
The correct option is **B**: \( \omega_2 < \omega_1 \).