看板Physics
标 题Re: 请问用费码定理证倒出光学中的司乃耳定律
发信站Local (Sat May 24 19:00:12 2003)
转信站Ptt!news.ntu!freebsd.ntu!netnews.csie.nctu!news.ee.nthu!tti
※ 引述《[email protected] (欧巴桑你个头)》之铭言：
: 请问有人知道吗
: 我们老师就丢下这几个字
: 我完全不知到他要干嘛
: 请问有人可以给一点提示吗?
: 拜托
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)
--
※ Origin: 乌龟岛<AntiGPL.Net> ◆ From: sw59-76-80.adsl.seed.net.tw