Are you over 40 and wonder what the magic amount of sleep every night might be? A new study arrives at an answer.

It turns out that seven hours of sleep a night may be the ideal amount for keeping your brain in good health if you're middle-aged or older.

"Getting a good night's sleep is important at all stages of life, but particularly as we age. Finding ways to improve sleep for older people could be crucial to helping them maintain good mental health and well-being and avoiding cognitive decline, particularly for patients with psychiatric disorders and dementias," said study author Barbara Sahakian, from the University of Cambridge's department of psychiatry, in England.

For the study, the investigators analyzed data on sleep patterns, mental health and well-being from nearly 500,000 British adults, aged 38 to 73, who completed a series of thinking tests. Brain imaging and genetic data were available for nearly 40,000 of the participants.

Seven hours of sleep per night was optimal for cognitive ("thinking") performance and mental health, according to the study published April 28 in the journal Nature Aging.

Participants who got too little or too much sleep did worse on tests that measure processing speed, visual attention, memory and problem-solving skills. They were also more likely to have symptoms of anxiety and depression, and worse overall mental well-being.

The study also found a link between amount of sleep and differences in the structure of brain regions involved in cognitive processing and memory, with greater changes associated with less or more than seven hours of sleep a night.

The findings suggest that too little or too much sleep may be a risk factor for mental decline as people age.

Previous studies have reported a link between amount of sleep and the risk of developing Alzheimer's disease and dementia.

"While we can't say conclusively that too little or too much sleep causes cognitive problems, our analysis looking at individuals over a longer period of time appears to support this idea," study author Jianfeng Feng, a professor at Fudan University in China, said in a Cambridge news release. "But the reasons why older people have poorer sleep appear to be complex, influenced by a combination of our genetic makeup and the structure of our brains."