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Question
Obtain the equation for apparent depth.
Solution
Light from object O at the bottom passes from denser (water) to rarer medium (air).
n1 and n2 are refractive of denser and rarer medium.
By snells law
n1 sin i = n2 sin r
sin i ≈ tan i, as i and r are small
n1 tan i ≈ n2 tan i
`"n"_1 "DB"/"DO" = "n"_2 "DB"/"DI"`
`"n"_1/"d" = "n"_2/"d'"`
`"d'"/"d" = "n"_2/"n"_1`
`"d'" = "n"_2/"n"_1 xx "d"`
If n2 = 1 and n1 = n
d' = `"d"/"n"`
d' - d = d`(1 - 1/"n")`
Apparent depth
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