Does a spherical wavefront thicken as it moves outwards ?

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The discussion centers on the behavior of spherical wavefronts of light as they propagate through different media. When a flash of light is emitted spherically, observers at varying distances may perceive differences in duration based on the medium. In a vacuum, the duration remains unchanged for all observers. However, in media like air, the duration can vary; distant observers may record longer or shorter pulses depending on the preparation of the light pulse.

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If a flash of light is emitted spherically and this is measured in terms of its duration by two distant observers with one twice as far away from the source as the other, and the source and observers are all at rest with respect to each other, will the flash appear to have the same duration for both observers.
 
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It depends on the shape of the flash and the medium the light is in. In vacuum, there is no change at all.

In most setups with a medium (for example, air), I would not expect any significant change
For very short pulses, the distant observer might record a longer pulse.
If you prepare the pulse in the correct way, the distant observer can observe a shorter pulse.
 

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