# Apparent Depth Problem

• larkinfan11
In summary, the problem involves finding the apparent depth of the bottom of a beaker filled with water and oil when observed from above. The equation used is Apparent Depth= d(n(observer)/n(object)). The first step is to solve for the apparent depth from the oil level to the water level, which is 22.2 cm. Then, the apparent depth from the air to the oil level is found to be 32.856 cm. However, the total apparent depth is incorrect and needs to be adjusted. The correct equation is 20/1.48 + 20/1.48 = 35 cm, and the final answer should be less than 35 cm.

## 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?

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

Andrew Mason said:
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?

larkinfan11 said:
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?
Not quite. Just consider the depth of an object at 20 cm below the oil only. What would the apparent depth be? What if the oil extended to 40 cm? (hint: 40/1.48 = 20/1.48 + 20/1.48)? Now think of those last 20 cm in water.

AM