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Shabbat 39a discusses cooking on Shabbat using the sun. It is permitted to roll an egg on a hot roof to cook it since this is not a typical way to cook, but you can't burry it in sun-heated-sand because you need to dig a hole to put it in the sand. Also, a handkerchief heated by the sun is ok because you don't need to dig to put the egg in. Rav Grossman adds in his Daf Yomi shiur that there was a machloket over cooking in microwaves on shabbat, they don't get hot, so it should be allowed, however since it is normal to cook using them it's prohibited.

So, can I use a parabolic dish to harness the sun's direct heat to cook on Shabbat?

How about a Fresnel Lens?

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As I understand it, the Talmud said there was no prohibition at all from cooking with direct sunlight; cooking on a solar-heated brick was prohibited because it looked like you were using an oven-heated brick.

With various lenses and reflectors, presumably you put the food in and then apply the lens; the cooking is with direct sunlight (albeit focused better), not a preheated surface. So I don't think it would fall under the rabbinic prohibition.

The more interesting question is that it may still be Biblically prohibited. As I heard in an mp3 from Rabbi Hershel Schachter, the novel reading of both Rabbis Moshe Feinstein and Joseph Soloveichik was that cooking by direct sunlight was only permissible because that wasn't a "normal" way of cooking at the time. (Rabbi Feinstein therefore felt that microwaving food would be a Torah prohibition; although it's been observed that when he wrote that a few decades ago, people thought that the microwave would completely replace the conventional oven; today microwave ovens are primarily handy for reheating, but don't do as much "real cooking" as their conventional counterparts.)

Therefore, if concentrated-solar cooking is normal, it would be Biblically prohibited. If abnormal, it would be allowed. How to define normal ... beats me (though my first inclination is that if it was normal, it wouldn't be on YouTube.)

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As I recall (and, unfortunately, I have no source handy for this, other than the Gemara cited in the question and the RaMBa"M below) the problem isn't merely the digging, but it is also an issue if the surface contributes to the cooking. If you were to, for example, use the hot hood of a car on a hot, sunny summer day to fry an egg, this might be a problem. If, however, you successfully placed the food item on a surface that did not absorb and radiate the heat back into the food and contribute to the cooking process, then it would be permissible.

The RaMBa"M seems to Pasken in Hilchoth Shabbath, 9:3-4 that it is Asur MiDeRabbanan to cook with alternate sources. Or am I reading that incorrectly (is my example of a car hood only MiDeRabbanan, but direct sunlight Mutar LeGamrei??)?

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