Question

Now use the expression found in Part C for the distance between your eyes and the object at point O, and find the ratio of the apparent distance to the real distance, d/D. Remember that the apparent distance is the distance calculated by your eyes using the angle θa instead of the angle θw. Since we are dealing with small angles, you may use the approximation sin(x)≈x and asin(x)≈x.

Answer 1

Hello your question is incomplete attached below is the missing part of the question

answer : ( d / D ) =
`n_(a)`

`n_(w)`

Explanation:

Given data:

Apparent distance = distance calculated using angle ∅a

also applying the approximation ; sin(x) ≈ x and asin(x) ≈ x

Find the ratio of apparent distance to real distance (d / D )

Using the given data in the question the ratio of apparent distance to real distance ( d / D ) =
`n_(a)`

`n_(w)`

where
`n_(a)` = index of refraction ( air )

`n_(w)` = index of refraction ( water )