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

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To determine the image position in a long glass rod with a convex hemispherical surface, the appropriate formula to use is 1/do + 1/di = (μ - 1)/R, where μ is the refractive index and R is the radius of curvature. The radius of curvature for the hemispherical surface is given as 3 cm, and the refractive index of the glass is 1.6. When calculating the focal length, it is important to note that f is not simply R/2 for spherical surfaces. The confusion arises from using the wrong assumptions about the focal length and the object distance, particularly when the object is at an infinite distance. Correct application of the formula should yield the correct image position.
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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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