Frances Elizabeth Somerville Alexander (née Caldwell; 13 December 1908 – 15 October 1958) was a British geologist, academic, and physicist, whose wartime work with radar and radio led to early developments in radio astronomy and whose post-war work on the geology of Singapore is considered a significant foundation to contemporary research. Alexander earned her PhD from Newnham College, Cambridge, and worked in Radio Direction Finding at Singapore Naval Base from 1938 to 1941. In January 1941, unable to return to Singapore from New Zealand, she became Head of Operations Research in New Zealand's Radio Development Lab, Wellington. In 1945, Alexander correctly interpreted that anomalous radar signals picked up on Norfolk Island were caused by the sun. This interpretation became pioneering work in the field of radio astronomy, making her one of the first women scientists to work in that field, albeit briefly.

Alexander was born Frances Elizabeth Somerville Caldwell on 13 December 1908 in Merton, Surrey. She spent some of her early life in India, where her father, Dr. K. S. Caldwell, was a professor at Patna College. (He was later principal of Patna Science College after its founding in 1928). In 1918, Alexander returned to the United Kingdom and began secondary school.

Alexander then attended Newnham College, Cambridge and studied natural science, initially focusing on physics. She was also offered a place at Somerville College, Oxford and Girton College, Cambridge. She graduated with First-class honours in 1931, then received a PhD in geology for a thesis on Aymestry Limestone, under the supervision of Owen Thomas Jones. She was a member of the Sedgwick Club, along with fellow female geologists, Dorothy Hill and Constance Richardson. Like all women graduates of Cambridge University at that time, she could not become a full member of the university until after equal rights were granted post 1945.

In July 1935, Alexander married a physicist, Norman Alexander, from New Zealand. When her husband took the post of Professor of Physics at Raffles College in Singapore, Elizabeth Alexander travelled there and began a study into the effects of weathering in the tropics. She was particularly interested in erosion and how, under certain circumstances, new rock seemed to be forming at unexpectedly high speed. She thus began experiments, burying samples in order to compare them with lab controls later. Whilst in Singapore, the Alexanders had three children, William in 1937, Mary in 1939 and Bernice in 1941.

Between 1940 and 1941, Alexander held the rank of Captain in the Naval Intelligence Service, working on radio direction-finding at Singapore Naval Base.

On 4 January 1942, under Navy orders to take her children to safety and return with specialist equipment being made in Australia, Dr. Alexander and her children were evacuated to New Zealand by a Short S23 C flying boat. After the Fall of Singapore on 15 February, she was stranded in New Zealand. She had no information about her husband for six months, and then was misinformed that he was dead. Whilst in New Zealand, Alexander became Senior Physicist and Head of the Operational Research Section of the Radio Development Laboratory in Wellington in 1942, where she remained until 1945. There she was responsible for most radio and radar research, including pioneering of radio meteorology in conjunction with Washington State College, development of the microwave radar program, and research on anomalous propagation leading to the post-war international project, Project Canterbury. In 1945, Alexander identified the "Norfolk Island Effect" as solar radiation. This discovery marked the beginning of Australian radio-astronomy after she left New Zealand when her contract ended with the end of the war in 1945.

There has been some debate over whether Alexander or Ruby Payne-Scott was actually the first woman to work in the field of radio astronomy. Despite her progress in the field, Alexander only ever considered radio astronomy a job and as soon as the war was over she returned to her passion of geology, never again working in radio astronomy.

Whilst Alexander worked in New Zealand, her husband had continued as Scientific Adviser to the Armed Forces, moving to help out at Singapore General Hospital when Raffles College was on the front line. At the hospital, he kept the X-ray machines going until Singapore fell a few days later. He was then interned in Changi, then Sime Road camps, along with the senior medical staff of the hospital.