Physics Question regarding Apparent Depth Really need assistance?

Question

I have no idea how to solve this problem and it is really frustrating me. Can anyone help me out with an explanation? I believe that it involves two applications of the apparent depth equation [apparent depth= d(Nobserver/Nobject)], but I'm not sure how to work it out. Any help would be greatly appreciated!!!

A beaker has a height of 40.0 cm. The lower half of the beaker is filled with water, 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?

Answer 1

Look, this problem is kind of easy, but I am gonna send you the graphic ok. Because, you need to use little angles, trigonometry, and twice the snell law:

http://img139.imagevenue.com/img.php?image=65571_scan0001_123_197lo.jpg

Ok, follow the graphic, what I did is find the little angles, because, the apparent distance, as you have notices is :

D = X

Now, You can find : tan(theta) = y / x

and you can find the value of y : y = 20tan(alpha) + 20tan(phi)

alpha is the first angle, starting from the bottom of the beaker, and phi, is the angle at the middle.

So you can use Snell's law, to find a relationship between these angles, and between theta.

Using the snell's law in :

Water - Oil

Oil - Air

You have that relationship :

1.3sin(alpha) = 1.48sin(phi)

1.48sin(phi) = 1*sin(theta)

Note : You know, using geometry, that you can move angles, between parallel lines.

then : the angles are little, so : tan = sin

y = 20sin(alpha) + 20(sin(phi)

y = xtan(theta)

X = apparent depht = 20( sin(alpha) / sin(theta)) + 20 ( sin(phi)/ sin(theta))

Using the relationships :

1.3sin(alpha) = 1.48sin(phi)

1.48sin(phi) = 1*sin(theta)

then : X = 28.8 cm >>> apparent depht

Hope that might help you, and the graphic.

Answer 2

obvious intensity is brought about by technique of the refraction of sunshine. obvious intensity is often below the genuine intensity. subsequently, a swimming pool continually looks shallower than that's. under no circumstances deeper. you may objective below the fish.