In which condition is a headlamp not required on a vehicle?

A vehicle is not required to have its headlamps on ½ hour after sunrise in clear conditions because this timeframe typically falls within daylight hours when natural light is sufficient for visibility. During this time, drivers can typically see clearly without the assistance of vehicle lights.

In contrast, the other conditions listed generally require the use of headlamps either because it is darker or because visibility is significantly reduced due to fog. For example, using headlamps in foggy conditions is crucial for safety, as standard visibility is compromised. Therefore, the clarity of conditions plays a significant role in determining the necessity of headlamps, making the specified option the correct one.