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In my basic science classes in high school, I have learned that during photosynthesis, plants absorb sunlight and produce food by converting carbon dioxide and water into sugar and starch.

To me, this seems similar to the analogy of solar cells that convert sunlight into electricity. When sunlight falls directly on the solar cell, it produces electricity, but even when it is cloudy with no direct sunlight available, electricity is produced, but with less efficiency.

So can photosynthesis occur in plants only when they are in direct sunlight or does photosynthesis also occur during cloudy weather when the light is diffuse or indirect?

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I recently took a trip to a nearby abandoned ore mine. Deep in there, I was surprised to see plenty of mosses around the installed neon tubes. So, photosynthesis does not even need actual sunlight to occur. I also agree with WYSIWYG's answer regarding the performance of leaves under diffuse light conditions. – Hav0k Jan 6 '15 at 8:29

Yes, photosynthesis does occur on cloudy days where the light exposure is diffuse - but the overall picture is not as simple as your solar cell analogy.

Consider one of the findings of the following article: "Impact of clear and cloudy sky conditions on the vertical distribution of photosynthetic CO₂ uptake within a spruce canopy" (Urban et al. 2011), where one of the findings is that

that shoots from deep within the canopy contribute substantially to the overall carbon balance during cloudy days. But, although shade-adapted shoots had a markedly positive carbon balance over a 24-h period on cloudy days, their performance was impaired on sunny days contributing only a marginal or even negative carbon balance from the middle and shaded parts of the canopy.

So, while leaves at the top of the canopy have a reduced rate of photosynthesis on cloudy days, leaves within the canopy and those that are shade-adapted, still photosynthesised.

I hope this helps a bit.

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Moreover, chlorophylls don't absorb all wavelengths equally. See here – WYSIWYG Jul 4 '13 at 14:42

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