Question

Obtain the equation for apparent depth.

Answer 1

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