and they are on opposite ends of the electromagnetic spectrum, then why can't light travel through walls which is right in the middle of the spectrum?  

This question has already been asked [here]( However, I am not entirely satisfied by the answer given on that page which relies on fanciful analogies and metaphors of ants, elephants etc. I am looking for a better explanation.  

I think the crux of the matter, and my dilemma, relates to formula for [penetration depth]( This is a well known formula used to explain the fact that low frequency waves have more penetration than high frequency waves.   

But then how come gamma waves have such high penetration?   

Are there some assumptions behind derivation of this formula which break when we consider very high frequency waves?  

Or, are there some new factors that need to be taken into account as we move into the high frequency regime?   

If given a radio source and a gamma source of equal intensity, then will the radio source have more penetrability than the gamma source per formula for [penetration depth]( If not, why not?