"His father had packed boxes of contact lenses in his rucksack in an outside pocket and he'd forgotten to take them out," she told This Morning. "He's lived on the fluid that the contact lenses...you know the little packs of contact lenses? He's literally lived on those packs of contact lenses for three nights."
Relatives said the teenager, a keen long-distance runner, owed his life to rescue workers who launched a massive helicopter search of the desolate region after he was reported missing from Upshot Station, near the town of Longreach, on Tuesday.
Mrs Woodhead, who travelled out to Australia, said: "I've spoken to Sam on the phone and I'm flying out to Longreach tomorrow morning."
She added: "I'm very, very relieved indeed. I've just had the worst three days of my life, and when I got the message from the pilot on the plane (that he had been located), I just cried."
The former Brighton College student, from Richmond upon Thames, in Surrey, was taken for a medical assessment before being transferred to a hospital in Longreach.