# Apparent Depth Problem

## Homework Statement

A beaker has a height of 40.0 cm. The lower half of the beaker is filled with water (n = 1.333), and the upper half is filled with oil (n = 1.48). To a person looking down into the beaker from above, what is the apparent depth of the bottom?

## Homework Equations

Apparent Depth= d(n(observer)/n(object))

## The Attempt at a Solution

I believe this is a two part problem, so I broke it down into that. First I solved it from the perspect of looking observing from the oil level to the water level and calculated this:

Apparent Depth= 20(1.48/1.333)=22.2

I used 20 as the distance between the water and the bottom because it was half of the size of the beaker. That may be incorrect, however.

I then used the apparent depth that I calcuated above to solve the second part from the aspect of looking at this from the air to the oil and calculated this:

22.2= d(1/1.48)
d=32.856

I then added the two together to get 55.056 cm as my total apparent depth, but the answer is incorrect. What am I doing wrong?

Andrew Mason
Homework Helper
The apparent depth should be shallower than the actual.

If the oil was not there, the depth would appear to be 20 + 20/1.33 = 35 cm. With the oil, what would it be?

AM

The apparent depth should be shallower than the actual.

If the oil was not there, the depth would appear to be 20 + 20/1.33 = 35 cm. With the oil, what would it be?

AM

I think I see what you're saying. With the oil there, the equation should look like this: 20/1.48 + 20(1.48/1.333) Am I on the right track?

Andrew Mason