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

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Homework Help Overview

The discussion revolves around determining the image position for an object placed at an infinite distance from a convex hemispherical surface of a long glass rod. The problem involves understanding the optics of refraction and the application of relevant formulas, specifically in the context of a glass medium with a given refractive index.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the use of the lens formula and question the application of the formula given the object distance is infinite. There is discussion about the correct formula to use, with some suggesting the standard lens equation and others proposing a specific formula related to the refractive index and radius of curvature.

Discussion Status

The discussion is ongoing, with participants sharing their calculations and questioning the correctness of their approaches. Some have provided values for the radius of curvature and refractive index, while others express confusion over the expected results and the application of formulas.

Contextual Notes

There is a lack of clarity regarding the expected answer and the correct application of the formulas, with participants questioning assumptions about the radius of curvature and the nature of the optical setup. The refractive index and dimensions of the rod are specified, but there may be misunderstandings about how to apply this information correctly.

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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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
 
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?
 
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
 
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?
 
its 3 cm,the answer expected in cm
 
fl415 said:
its 3 cm,the answer expected in cm
Then f is 5 cm.
 
f is 1.5...right? its radius /2
 
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.
 

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