看板Physics
標 題Re: 請問用費碼定理證倒出光學中的司乃耳定律
發信站Local (Sat May 24 19:00:12 2003)
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※ 引述《[email protected] (歐巴桑你個頭)》之銘言：
: 請問有人知道嗎
: 我們老師就丟下這幾個字
: 我完全不知到他要幹嘛
: 請問有人可以給一點提示嗎?
: 拜託
dt = ds / v = n(y) ds / c
n(y) = index of refraction, which depends on y
ds = sqrt[ 1+y(x)'^2 ] dx
y(x)' = dy(x) / dx
time = S dt
= S n(y) sqrt[ 1+y'^2 ] / c dx from x1 to x2
= S F(y,y') / c dx
According to Fermat's principle of least time
and calculus of variations,
F - y'(@F/@y') = constant ( @ = partial derivative )
n(y) / sqrt[ 1+y'^2 ] = constant
Let y' = cot(theta)
theta = angle between y-axis and the tangent of y(x)
n(y) sin(theta) = constant
n1 sin(theta1) = n2 sin(theta2)
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※ Origin: 烏龜島<AntiGPL.Net> ◆ From: sw59-76-80.adsl.seed.net.tw