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Question Number 47713 by ajfour last updated on 13/Nov/18

Commented by ajfour last updated on 13/Nov/18

If cylinder has length L, find  how much area of cylinder  receives light from the point  source at a distance d and at  same level h=R as its axis.  ( instead of h=(R/2) in diagram  ).

$${If}\:{cylinder}\:{has}\:{length}\:{L},\:{find} \\ $$$${how}\:{much}\:{area}\:{of}\:{cylinder} \\ $$$${receives}\:{light}\:{from}\:{the}\:{point} \\ $$$${source}\:{at}\:{a}\:{distance}\:{d}\:{and}\:{at} \\ $$$${same}\:{level}\:{h}={R}\:{as}\:{its}\:{axis}. \\ $$$$\left(\:{instead}\:{of}\:{h}=\frac{{R}}{\mathrm{2}}\:{in}\:{diagram}\:\:\right). \\ $$

Commented by mr W last updated on 13/Nov/18

A_(lighted) =2θRL=2RL cos^(−1) (R/d)

$${A}_{{lighted}} =\mathrm{2}\theta{RL}=\mathrm{2}{RL}\:\mathrm{cos}^{−\mathrm{1}} \frac{{R}}{{d}} \\ $$

Commented by mr W last updated on 14/Nov/18

Commented by ajfour last updated on 14/Nov/18

Thank you Sir, i understood my  poor recognition!

$${Thank}\:{you}\:{Sir},\:{i}\:{understood}\:{my} \\ $$$${poor}\:{recognition}! \\ $$

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