Refraction at a spherical surface

In summary, the conversation is discussing the apparent position of a fish in a spherical fish bowl, taking into account the index of refraction of air and water. The equation for this calculation is (n_a/s) + (n_b/s_prime) = 0, but it is only applicable for a flat surface. The correct equation for a spherical surface is \frac{n_1}{s}+\frac{n_2}{s'}=\frac{n_2-n_1}{R}.
  • #1
sghaussi
33
0
hello again:

A Spherical Fish Bowl. A small tropical fish is at the center of a water-filled spherical fish bowl 28.0 cm in diameter.

Find the apparent position of the fish to an observer outside the bowl. The effect of the thin walls of the bowl may be ignored.


i'm dealing with the formula : (n_a/s) + (n_b/s_prime) = 0

n_a = index of refraction of air (1.00) ?
n_b = index of refraction of water (1.33)?
s = position of fish = 14 cm ?
s_prime = position of image?

I tried plugging into the above formula, however I keep getting the wrong answer. Also, I tried switching n_a with n_b but that also didn't work. I'm thinking that the position of my fish isn't 14 cm? What am I doing wrong?
 
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  • #2
sghaussi said:
i'm dealing with the formula : (n_a/s) + (n_b/s_prime) = 0

That equation is only for a flat surface. More generally, it's:

[tex]\frac{n_1}{s}+\frac{n_2}{s'}=\frac{n_2-n_1}{R}[/tex]

where R is the radius of curvature of the bowl.
 
  • #3



Hello there,

The formula you are using is correct, but the position of the fish is not 14 cm. In this problem, we are dealing with a spherical surface, so the position of the fish needs to be measured from the center of the sphere, not from the surface. Since the fish is at the center of the bowl, its position would be 0 cm.

So, the correct formula to use would be: (n_a/s) + (n_b/s_prime) = 0, where s = 0 cm.

Plugging in the values, we get: (1.00/0) + (1.33/s_prime) = 0
Solving for s_prime, we get: s_prime = 0 cm.

This means that the image of the fish would also be at the center of the bowl, at a distance of 0 cm from the surface. This is because light rays passing through a spherical surface are not bent, but instead continue in a straight line.

I hope this helps clarify the problem for you. Let me know if you have any further questions.
 

1. What is refraction at a spherical surface?

Refraction at a spherical surface refers to the bending of light rays as they pass through a spherical surface, such as a lens or a curved mirror.

2. What causes refraction at a spherical surface?

Refraction at a spherical surface is caused by the change in speed of light as it passes from one medium to another. This change in speed causes the light rays to bend.

3. How does the shape of a spherical surface affect refraction?

The shape of a spherical surface can determine the degree and direction of refraction. A convex surface will cause light rays to converge, while a concave surface will cause them to diverge.

4. What is the relationship between the angle of incidence and the angle of refraction at a spherical surface?

The angle of incidence and the angle of refraction are related by Snell's Law. This law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speeds of light in the two media.

5. How does refraction at a spherical surface affect the image formed?

Refraction at a spherical surface can cause the image formed by the lens or mirror to appear larger, smaller, or distorted. The degree of distortion depends on the curvature and thickness of the surface, as well as the angle of incidence of the light rays.

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