Một cái máng nước sâu 60m, rộng 80m có hai thành bên thẳng đứng. Đúng lúc máng cạn nước thì bóng râm của thành AB kéo dài tới đúng chân C thành CD đối diện. Người ta đổ nước vào máng đến một độ cao h thì bóng của thành AB ngắn bớt đi 14cm so với trước. Chiết suất của nước là 4/3. Tính h.

1 câu trả lời

Đáp án:

$h=24cm$

Giải thích các bước giải:

$AB=60m;BC=80m;n=\dfrac{4}{3}$

khi không có nước:

$\begin{align}
  & \tan i=\dfrac{CB}{AC}=\dfrac{80}{60} \\ 
 & \Rightarrow i={{53}^{0}} \\ 
\end{align}$

theo định luật khúc xạ ánh sáng:

$\begin{align}
  & \sin i=n.\operatorname{s}\text{inr} \\ 
 & \Rightarrow \operatorname{s}\text{inr}=\dfrac{\sin {{53}^{0}}}{\dfrac{4}{3}}=0,6 \\ 
 & \Rightarrow r=36,{{87}^{0}} \\ 
\end{align}$

$\begin{align}
  & \tan i=\dfrac{HB}{IH} \\ 
 & \operatorname{t}\text{anr}=\dfrac{HB-RB}{h} \\ 
 & \Rightarrow \dfrac{\tan i}{\operatorname{t}\text{anr}}=\dfrac{HB}{HB-RB}=\dfrac{16}{9} \\ 
 & \Rightarrow \dfrac{HB}{HB-14}=\dfrac{16}{9} \\ 
 & \Rightarrow HB=32cm \\ 
\end{align}$

độ cao h: 

$IH=h=\dfrac{HB}{\tan i}=\dfrac{32}{\tan 53}=24cm$

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