Refraction by a transparent spherical surface

In summary, the index of refraction for a transparent sphere can be determined by using the equation that relates object distances and image distances for spherical surfaces. In this case, the index of refraction was found to be 2.00.
  • #1
bcjochim07
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Homework Statement


Parallel light rays enter a transparent sphere along a line passing through the center of the sphere. The rays come to a focus on the far surface of the sphere. What is the sphere's index of refraction?


Homework Equations





The Attempt at a Solution


so I used the equation that relates object distances and image distances for spherical surfaces: n1/s + n2/s' = (n2-n1)/R

I am calling the radius of the sphere R

(1.00)/s + n2/2R = (n2-1.00)/R and I think for this case s[tex]\rightarrow[/tex][tex]\infty[/tex]
so n2/2R = (n2-1)/R
n2 = 2(n2-1)
n2 = 2n2 -2
-n2=-2
so n2= 2.00 Is this correct?
 
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  • #2
Looks fine to me. :smile:
 
  • #3



Your approach and calculation are correct. The sphere's index of refraction is indeed 2. This means that the speed of light is twice as slow inside the sphere compared to outside. This phenomenon is known as refraction, where light bends as it passes through a medium with a different index of refraction. It is a fundamental concept in optics and has many practical applications, such as in lenses and prisms. Keep up the good work!
 

1. What is refraction by a transparent spherical surface?

Refraction by a transparent spherical surface is the bending of light as it passes through a curved, transparent surface such as a glass or water sphere. This is caused by a change in the speed of light as it moves from one medium to another.

2. How does the curvature of the spherical surface affect refraction?

The curvature of the spherical surface plays a significant role in refraction. A more curved surface will cause a greater bending of light, while a flatter surface will cause less bending. This is due to the change in angle at which the light hits the surface and the different speeds of light in different parts of the curved surface.

3. What is the difference between convex and concave refraction?

Convex refraction occurs when the curved surface is thicker in the middle and thinner at the edges, causing light to converge at a focal point. Concave refraction, on the other hand, occurs when the curved surface is thinner in the middle and thicker at the edges, causing light to diverge as it passes through the surface.

4. What is the relationship between the angle of incidence and the angle of refraction?

The angle of incidence is the angle at which light hits the curved surface, and the angle of refraction is the angle at which the light is bent as it passes through the surface. These two angles are related by Snell's law, which 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 mediums.

5. How does refraction by a transparent spherical surface affect the appearance of objects?

Refraction can cause objects to appear distorted or magnified, depending on the curvature of the spherical surface and the angle at which the light hits it. This is why objects viewed through a curved glass or water sphere may appear larger or distorted compared to when viewed directly. This effect is also used in optical instruments such as magnifying glasses and telescopes.

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