Lens with different refraction index on each side

• JoeyBob
In summary, the conversation discusses a formula for calculating the location of an image based on refraction indexes and the actual and virtual locations. The correct formula is n1/p+n2/q=-(n2-n1)/R, but the calculation for n2-n1 was incorrect. The correct answer is q = 60.88 cm above the water.
JoeyBob
Homework Statement
see attached
Relevant Equations
1/p+1/q=-2/R
So I am not really familiar with lens questions when there's 2 different refraction indexes. I tried using n1/p+n2/q=-(n2-n1)/R but it doesn't seem to work.

p would be the actual location of the fly and q would be the virtual location, what the fish sees if I am understanding correctly. n1 would be the index of refraction where the fly is and n2 where the virtual image is?

So 1/60+1.3/q=-1.3/64. q=-35.155

So the image is 35.155 cm above the water. But this is wrong, the answer is 60.88 cm

Attachments

• question.PNG
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JoeyBob said:
n1/p+n2/q=-(n2-n1)/R

So 1/60+1.3/q=-1.3/64
The 1.3 on the right side is not correct.

TSny said:
The 1.3 on the right side is not correct.
The rest is correct then?

Shouldn't it be on top according to the formula?

The rest is correct.

JoeyBob said:
Shouldn't it be on top according to the formula?
I'm not sure what you are asking here.

n1/p+n2/q=-(n2-n1)/R

is this formula incorrect here?

The formula looks correct, although I’m not sure what sign conventions you are using for R, etc.

You made a mistake in calculating ##n_2-n_1##.

JoeyBob
TSny said:
The formula looks correct, although I’m not sure what sign conventions you are using for R, etc.

You made a mistake in calculating ##n_2-n_1##.
ya I am dumb. 1.3-1 isn't the same as 1.3-0. I get q = -60.88 when I use 0.3, so 60.88 above the water.

Thanks.

berkeman
JoeyBob said:
ya I am dumb.
Not at all. We all make slips like this

1.3-1 isn't the same as 1.3-0. I get q = -60.88 when I use 0.3, so 60.88 above the water.
Thanks.
Looks good.

1. What is a lens with different refraction index on each side?

A lens with different refraction index on each side is a type of lens where the refractive index, or the measure of how much light is bent as it passes through the lens, is different on each side. This means that the lens will bend light at different angles depending on which side the light enters from.

2. How does a lens with different refraction index on each side work?

A lens with different refraction index on each side works by bending light as it passes through the lens. The change in refractive index on each side causes the light to bend at different angles, which allows the lens to focus or disperse light depending on its design.

3. What are the applications of a lens with different refraction index on each side?

A lens with different refraction index on each side has a variety of applications in optics, including in cameras, microscopes, telescopes, and eyeglasses. These lenses can also be used in scientific experiments and in the production of precision instruments.

4. How is the refraction index determined for each side of the lens?

The refraction index for each side of the lens is determined by the material that the lens is made of. Different materials have different refractive indices, and the thickness of the lens can also affect the refractive index. The refractive index can be calculated using Snell's law, which relates the angle of incidence and refraction of light passing through a boundary between two materials.

5. Are there any disadvantages to using a lens with different refraction index on each side?

One potential disadvantage of using a lens with different refraction index on each side is that it can introduce chromatic aberration, which is the distortion of colors in an image. This can be minimized by using multiple lenses with different refractive indices, or by using special coatings on the lens. Additionally, these lenses may be more complex and expensive to manufacture compared to lenses with a uniform refractive index.

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