# Optics thick lens question

A window of a submarine is 30 cm thick, and is underwater. The index of refraction of the window is 1.65. The index of refraction fo th eocean is 1.35. The index of refraction inside the submarine is 1.00.

A scuba diver is 1 meter away from thw window. Where does his image form?

I used n1/d_o + n2/d_i = (n2-n1)/R (this goes to zero since R is infinity), from the Thick Lens Equation.

1.35/100 = -1.65/d_i

d_i = -122.22

Now d_o2 = 152.22, because of the thickness thing (d_i+d_o2 = thickness)

Again;

n/d_o2 + n/d_i2 = (some n - some n)/infinity (goes to zero again)

Which n values do I use? Is it 1.65/152.222 + 1/d_i2 =0
or is it 1.65/152.222+1.35/d_i2 =0 ??

Simon Bridge
Homework Helper
You need all three n values to solve this problem.
Does the thick lens equation allow for the refractive index being different on each side of the lens?
It may help you to draw a sketch of the problem - maybe with two diverging rays from the diver position and dotted lines traced back to locate the image.

Thanks Mr. Bridge...long time no see!
I could not find any specifications of the thick lens equation online or in my textbook...I understand it is derived from lensmakers.

I drew a diagram, and light seems to pass through the ocean--to the glass---to the air.

Is my solution correct then? To me it makes sense because if we were NOT to use n=1, the situation would be analogous to putting it just in water (which obviously gives a different distance :p).

Simon Bridge
Homework Helper
You can look up the derivation of the thick-lens formula online.
You seem to be guessing rather than reasoning to the answer ...

You can try using Snell's law to find how a ray of light bends through each interface.
Is it safe to ignore one of the refractive indeces?

Snells law would require two bends---the first from ocean to glass and then from glass to air. Thats my reasoning wit using 1.

I tried doing stuff with beams of light, but cant get an answer since the lens is not curved
It is definitely NOT safe to ignore an n.

Im fairly confident my dea is correct theoretically.

Now im not certain if i put it into the equation correctly. I still cannot find any derivation.

Additionally, my answer makes sense conceptually because the image is now closer to the lens.

Am i right?

Dale
Mentor
2020 Award
I would just use Snell's law twice. Once from ocean to window and once from window to air.

How do you use snell's law?? Since the surface is not curved, the incident angle (90 degrees) will be the same as the refracted angle (since n1sinx1=n2sinx2)

Dale
Mentor
2020 Award
Think about how binocular vision works with depth perception. Is it actually true that the incident angle is 90 deg?

I don't think I have learned that yet....
is there any way to use the thick lens equation (as I did in my first post)? Or is it incorrect? (also why is it incorrect if it is?_

Simon Bridge
Homework Helper
I don't think I have learned that yet....
You have seen a diagram deriving the apparent depth equation haven't you?

How do you use snell's law?? Since the surface is not curved, the incident angle (90 degrees) will be the same as the refracted angle (since n1sinx1=n2sinx2)
In optics, angles are measured from the normal to the surface - not from the surface itself.

Light rays fan out from the object in all directions.
All you need is any two rays that do not have a 0 deg angle of incidence in order to use Snell's law.

is there any way to use the thick lens equation (as I did in my first post)? Or is it incorrect? (also why is it incorrect if it is?_
This is what we are trying to get you to see.

Before you can use an equation, you need to understand it.
The thick lens equation was derived assuming that there was the same refractive index on either side of the lens - this gives a reason why you shouldn't expect it to work. But it may do - you don't know because you don't understand the equation. Part of the point of your homework is to gain understanding - so if we just tell you stuff right out, it will defeat the point of your education.

You have said:
It is definitely NOT safe to ignore an n.
Im fairly confident my dea is correct theoretically.
You say you cannot ignore an n. There are three n's, but the thick lens equation (the one you wrote down for us) only uses two doesn't it?
So if you use it, it means ignoring one of the three n's you are given.
Something you also say is not safe.

So how can you be so confident that it is right to do so?

You need a way to check your ideas:
The way to check is to use Snell's law on carefully chosen light rays.
Go look at your notes for the apparent depth problem and see how that was done - your working should be the same, only you have two surfaces. You need two light-rays that diverge from the object.

Here's some tutorials:
http://www.schoolphysics.co.uk/age11-14/Light/text/Real_and_apparent_depth/index.html [Broken]
http://www.physicstutorials.org/home/optics/refraction-of-light/apparent-depth-real-depth

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