At first glance, the solar electric industry looks like a certified success story for American business.

The price of photovoltaic cells -- the silicon wafers that produce an electric current upon contact with sunlight -- has dropped dramatically in the past decade, thanks to impressive scientific advances. Sales have grown to $50 million a year worldwide, with a dozen American firms the unquestioned leaders.

The units now are practical for use in remote areas where electric power lines don't reach, and industry officials speak confidently of further technological leaps that can make photovoltaic power as cheap as electricity from coal by 1990.

That is, provided the Reagan administration doesn't pull the plug. Since its beginnings following the 1973 Arab oil embargo, the solar industry has been nourished with streams of federal grants, subsidies and tax incentives. Congress approved a 10-year, $1.5 billion aid program three years ago, and President Carter dedicated a $28,000 solar heater on the White House roof to symbolize the connection.

All that is changing.

The Energy Department, cutting hard on fiscal year 1983 spending plans, is expected to slash direct federal grants to solar energy firms and may eliminate them entirely if the department follows the "shutdown case" being prepared by its budget staff.

Even more threatening to the solar industry is the possible loss of special tax credits and deductions for homeowners and businesses that buy solar equipment. These tax breaks were designed to boost sales of solar equipment by lowering the effective purchase price with tax subsidies. They are the key to the industry's future growth, according to industry representatives who testified before the Senate energy committee last week.

But the Treasury Department, scrambling to find revenues to shrink future budget deficits, is aiming at the energy tax credits and is likely to propose legislation to eliminate some, if not all, of them, administration officials say.

Although the industry would not die, technological development would slow dramatically, and the arrival of cheap solar electric power would fade beyond the horizon, industry officials warn.

The Reagan administration says simply that the solar energy industry is ready to stand on its own and the government is no longer handpicking favored new energy technologies for federal support.

Not surprisingly, the industry's view of a future without tax credits is very dark.

"The lead of the U.S. photovoltaics industry is eroding, and it is being challenged by foreign competitors," industry consultant Peter Glaser of Arthur D. Little Inc. said at last week's Senate hearings. Continued government support is needed, he said.

The lead will be lost if the federal government is content to sit back, waiting for the major scientific breakthrough that would make solar power cost-competitive with electricity from other sources, said William E. Bicker, spokesman for Arco Solar Industries, a subsidiary of Atlantic Richfield.

The growing need for electric power in remote areas of developing countries provides the first significant opportunity for expansion in the solar electric industry, Bicker said. If the American firms lose this market to their Japanese, French and West German competitors, they could fall behind and out of the race for good, Bicker added. And the U.S. firms can't compete abroad if sales of photovoltaic devices in the United States dry up, he concluded.

To keep the U.S. market healthy, he called for greater tax credits for commercial photovoltaic investments: Companies now get a 15 percent special energy investment tax credit for purchasing solar and other renewable energy devices. Bicker and Arco would like that credit doubled for the next five years.

The particular technological challenges of photovoltaic power make federal support the key to significant cost reductions and rapid commercial development, says John Goldsmith of Solarex Corp. of Rockville, one of the industry's leading firms.

The first photovoltaic cells were formed from pure silicon crystals, drawn from cauldrons of molton silicon. The basic element in sand and one of the earth's most abundant materials, silicon must be highly purified for use in energy cells, and companies had to find faster ways of making the crystalline form.

With breakthroughs in crystal technology, the cost of producing electric power from a solar cell has dropped from $100 a watt nine years ago to less than $10 now, Goldsmith said. A comparable reduction lowering the price to $1 a watt would make solar electric power competitive with other forms of electricity, he said, and purification of silicon is an essential remaining step.