the angle i with the original direction. The angle i can be measured, and we are then in a position to calculate the value of n, i.e. the index of refraction for light passing from air into the liquid.
We know the index n for air/glass :
N (= 1-61) = -?5^.
sin r
For the light entering the glass from the liquid the angle of incidence is 90° (sin i x = 1), and we can calculate, the index n x liquid/glass in the following manner :
��• •
��„, = «?.*! = _,
��sm^ sm r x Now, by trigonometry,
��sin r, = cos r = */ 1 - sin 2 r
��• •
��and, by transposing the first equation, sin r = —5.?, there-
N
fore,
��sin r x = ^ / 1~ —2~> an ^ consequently =
��s/ n 2 — sin 2 i
��therefore n x =
��N N
��<s/ n 2 — sin 2 ^
If now we remember that n = --, then we find the
n x
index for air /liquid = n = */n 2 — sin 2 i. There are tables which give the values of n directly for each value of i.
We thus obtain the index air /liquid, but if we wish to obtain the absolute index of refraction from vacuum into the liquid the value found must be multiplied by 1*00029. This correction, however, is generally omitted.
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