Geometric Q: Determine Image Position in Long Glass Rod w/ Refractive Index

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In summary, the question is asking for the position of an image when an object is placed at an infinitely far distance to the left of a glass rod's convex hemispherical surface. The formula to use is 1/do + 1/di = (μ - 1)/R, where μ is the refractive index and R is the radius of curvature of the hemisphere. The expected answer is 3 cm and the expected value for f is 5 cm. However, f = r/2 is only true for concave mirrors, not for spherical surfaces.
  • #1
fl415
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the questions is
The left end of a long glass rod in diameter has a convex hemispherical surface in radius. The refractive index of the glass is . Distances are measured from the vertex of the hemispherical surface (to the right is positive for image distances).

Determine the position of the image if an object is placed in air on the axis of the rod at the infinitely far distance to the left of the vertex of the curved end.

do i use 1/d+1/d_i=1/f? or i use something else? i plug in 1/d which d is infinity, so its 0, but i didnt get the right answer. can anyone help?
 
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  • #2
fl415 said:
the questions is
The left end of a long glass rod in diameter has a convex hemispherical surface in radius. The refractive index of the glass is . Distances are measured from the vertex of the hemispherical surface (to the right is positive for image distances).

Determine the position of the image if an object is placed in air on the axis of the rod at the infinitely far distance to the left of the vertex of the curved end.

do i use 1/d+1/d_i=1/f? or i use something else? i plug in 1/d which d is infinity, so its 0, but i didnt get the right answer. can anyone help?
Use the formula
1/do + 1/di = (μ - 1)/R
 
  • #3
its still wrong, i plug in 1/d_i=(1.6-1)/3 which give me 5 and its wrong. you got any other ideas?
 
  • #4
the question is

The left end of a long glass rod 6cm in diameter has a convex hemispherical surface 3cm in radius. The refractive index of the glass is 1.6 . Distances are measured from the vertex of the hemispherical surface (to the right is positive for image distances).

i don't know why it didnt show up number at first
 
  • #5
fl415 said:
its still wrong, i plug in 1/d_i=(1.6-1)/3 which give me 5 and its wrong. you got any other ideas?
What is the radius of curvature of the hemisphere? What is the expected answer?
 
  • #6
its 3 cm,the answer expected in cm
 
  • #7
fl415 said:
its 3 cm,the answer expected in cm
Then f is 5 cm.
 
  • #8
f is 1.5...right? its radius /2
 
  • #9
fl415 said:
f is 1.5...right? its radius /2
No. f = r/2 is true for the concave mirrors only, not for the spherical surfaces.
 

Related to Geometric Q: Determine Image Position in Long Glass Rod w/ Refractive Index

1. What is a geometric determination of image position?

A geometric determination of image position refers to the process of using geometric principles, such as the laws of reflection and refraction, to calculate the location of an image formed by a curved or refractive surface.

2. How do you determine the image position in a long glass rod?

To determine the image position in a long glass rod, you will need to know the refractive index of the glass and the angle of incidence of the light ray entering the rod. Using the laws of refraction, you can calculate the angle of refraction and use it to determine the location of the image within the rod.

3. What is the refractive index of a material?

The refractive index of a material is a measure of how much the speed of light is reduced when traveling through that material. It is a dimensionless quantity and is typically denoted by the symbol "n". The higher the refractive index, the slower the speed of light in that material.

4. What factors can affect the image position in a long glass rod?

The image position in a long glass rod can be affected by the refractive index of the glass, the angle of incidence of the light ray, and the curvature of the rod. Additionally, the length and diameter of the rod can also play a role in determining the image position.

5. Why is it important to determine the image position in a long glass rod?

Determining the image position in a long glass rod is important for understanding the behavior of light rays as they travel through different materials. It also has practical applications in the design and construction of optical devices, such as lenses and mirrors.

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