Introduction:
An auto-transformer is a type of transformer that has a single winding with multiple taps. It is used to step up or step down the voltage level depending on the requirement. In the case of a sodium vapor lamp, a high leakage reactance is desired in the auto-transformer.

Explanation:
The sodium vapor lamp is a type of gas discharge lamp that requires a high starting voltage to initiate the discharge. Once the discharge is initiated, the lamp operates at a lower voltage level. To achieve this, an auto-transformer is used with the lamp.

Step-up Ratio:
If the auto-transformer has a high step-up ratio, it means that the output voltage will be significantly higher than the input voltage. This is not desirable for a sodium vapor lamp because it requires a high starting voltage but operates at a lower voltage level. A high step-up ratio would result in an excessively high operating voltage, which can damage the lamp.

Step-down Ratio:
If the auto-transformer has a high step-down ratio, it means that the output voltage will be significantly lower than the input voltage. This is also not desirable for a sodium vapor lamp because it needs a high starting voltage to initiate the discharge. A high step-down ratio would result in a lower starting voltage, which may not be sufficient to start the lamp.

Leakage Reactance:
Leakage reactance refers to the inductive reactance present in the transformer due to the leakage flux. A high leakage reactance in the auto-transformer helps in limiting the starting current and providing a higher starting voltage to the lamp. This is important for the proper operation of the sodium vapor lamp.

Resistance:
Resistance in the auto-transformer is not directly related to the starting voltage or the operation of the sodium vapor lamp. While it is important to have low resistance to minimize power losses in the transformer, it does not have a significant impact on the starting voltage or operation of the lamp.

Conclusion:
In conclusion, an auto-transformer used with a sodium vapor lamp should have a high leakage reactance. This helps in limiting the starting current and providing a higher starting voltage to initiate the discharge in the lamp. A high step-up or step-down ratio is not desirable for the proper operation of the lamp. Resistance does not have a significant impact on the starting voltage or operation of the lamp.