Index of refraction in an air bubble

[tiger1]

[SOLVED] Index of refraction

Homework Statement

An air bubble inside an 9.00 cm-diameter plastic ball is 2.90 cm from the surface.

As you look at the ball with the bubble turned toward you, how far beneath the surface does the bubble appear to be?

Homework Equations

n_1/s + n_2/s' = n_2-n_1/R

The Attempt at a Solution

1.59/.0290 + 1/s' = 1-1.5/.045
s'=1.52

I'm not sure why that isn't correct.

...

1.59/.0290+1/s' = 1.59-1/.045
s'=.024m <- correct

 

[rl.bhat]

Here s' is virtual. So it should be -ve.
Your value is correct.

 

[tomcue]

I would like to clarify that the index of refraction is a measure of how much light is bent as it passes through a material. The equation provided is the Snell's law, which relates the angles of incidence and refraction to the indices of refraction of two materials. In this situation, the air bubble is surrounded by air and a plastic material, so we can use the equation n1sinθ1 = n2sinθ2 to calculate the index of refraction for the air bubble.

Given the diameter of the plastic ball and the distance of the air bubble from the surface, we can use the formula for the volume of a sphere to calculate the volume of the air bubble. Then, using the formula for the volume of a sphere, we can calculate the radius of the air bubble. From there, we can calculate the angle of refraction using the given distance of the bubble from the surface and the radius of the air bubble.

However, without knowing the angle of incidence, we cannot accurately determine the index of refraction for the air bubble. Additionally, the index of refraction for air is very close to 1, so the difference in index of refraction between the air and the plastic material may not have a significant effect on the apparent position of the air bubble. Therefore, the solution provided may not be entirely accurate.

In conclusion, while the provided solution may be correct, it is important to consider all factors and clarify any uncertainties when solving problems related to the index of refraction.