Refraction at spherical surface

In summary, the problem involves a semi-circle shaped cylindrical glass block with a radius of curvature of 10.0cm and a refractive index of 1.50. A pin is placed at the center of curvature O, and the question is asking how far from the surface the pin appears when viewed along the axis of the spherical surface. The solution involves considering rays from the tip of the pin to points on the surface of the sphere and using the tangent plane to determine the path of the ray within the sphere. Depending on whether the rays intersect at a single point, the image of the tip of the pin can be determined. There is also a discrepancy in the notes about the sign of the radius of curvature, with one source saying
  • #1
desmond iking
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Homework Statement



A semi-circle shaped cylindrical glass block has a radius of curvature of 10.0cm. and a refractive index of 1.50 as shown. A pin is placed at the centre of curvature O . How far from the surface do the pin appear to be when it is viewed along the axis of the spherical surface?


Homework Equations





The Attempt at a Solution


The diagram is in the photo and the solution is in the photo , p/s : this is the notes from my senior.
from the digram , I know that the object is placed on the left , whereas the refracting surface is concave relative to the the object . (assume the light pass from left to right). in the photo 2 , i was told that if refracting surface is concave relative to the the object , then the radius of curvature is negative... but here, the notes give the radius of curvature is positive. which on is correct? can someone help please?
 

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  • #2
Pick several points on the surface of the sphere and consider rays from tip of the pin to each point. Use the tangent plane at each point to determine the path of the ray within the sphere. If they all intersect at a single point that is the image of the tip of the pin. If they do not intersect at a single point, there is no image. Do the same for the other end of the pin.
 
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  • #3
HallsofIvy said:
Pick several points on the surface of the sphere and consider rays from tip of the pin to each point. Use the tangent plane at each point to determine the path of the ray within the sphere. If they all intersect at a single point that is the image of the tip of the pin. If they do not intersect at a single point, there is no image. Do the same for the other end of the pin.

which on is correct? the radius of curvature is positive or negative?
 

Related to Refraction at spherical surface

1. What is refraction at a spherical surface?

Refraction at a spherical surface is the bending of light as it passes through a curved interface between two different mediums, such as air and water.

2. How does the angle of incidence affect refraction at a spherical surface?

The angle of incidence, which is the angle between the incident ray and the normal line of the surface, determines the amount of bending that occurs during refraction. A larger angle of incidence will result in a greater amount of refraction.

3. What is the difference between convex and concave refraction at a spherical surface?

Convex refraction occurs when light passes through a convex surface, such as a glass lens, and is bent towards the center of the sphere. Concave refraction occurs when light passes through a concave surface, such as the surface of a spoon, and is bent away from the center of the sphere.

4. How is the refractive index of a medium related to refraction at a spherical surface?

The refractive index of a medium is a measure of how much the speed of light is reduced when passing through that medium. The greater the difference in refractive index between two mediums, the greater the amount of refraction that will occur at a spherical surface between them.

5. What are some real-life applications of refraction at a spherical surface?

Refraction at a spherical surface is used in various optical instruments, such as eyeglasses, microscopes, and telescopes. It is also essential in understanding the formation of images in the human eye and in the design of contact lenses.

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