Image of an Object Inside Hollow Glass Sphere

In summary, the question asks for the index of refraction of a glass sphere with an empty sphere inside, and the focal point of this optical system. The solution provided uses a thick lens formula instead of the thin lens formula that was attempted.
  • #1
Kaan99
2
0
Hello,
This question is from 1990 Turkey National Physics Olympics. I tried my best to translate it clearly.

1. Homework Statement

https://s23.postimg.org/cotn29afv/Hollow+Spherical+Glass.jpg

The sphere of radius 2R has an empty sphere inside with radius R. In order for the image of an object on the inner surface of the sphere to be R/5 far away from the object (which is shown with an asterisk*) for an observer at the indicated position (göz), what should be the index of refraction of the glass? Where is the focal point of this optical system?

Homework Equations


Thin Lens Equation
Lensmaker's Equation

The Attempt at a Solution


The lens is made up of to circles of radii R and 2R, using lensmaker and thin lens eq.
## \frac{1}{f} = (n-1) (\frac{1}{R_1}-\frac{1}{R_2})=\frac{1}{d_o}+\frac{1}{d_i}##
## (n-1)(\frac{1}{-R}-\frac{1}{-2R})=\frac{1}{2R}+\frac{1}{d_i}##
## \frac{n-1}{-2R}=\frac{1}{2R}+\frac{1}{d_i}##
## d_i=\frac{n}{-2R}##

It turned out that my attempt wasn't accurate from the start, as it deviates from the solution provided. I couldn't understand how the first equation is formed in the solution.

The result is n=2 and f=4R.
 
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  • #2
Kaan99 said:

The Attempt at a Solution


The lens is made up of to circles of radii R and 2R, using lensmaker and thin lens eq.
1f=(n−1)(1R1−1R2)=1do+1di1f=(n−1)(1R1−1R2)=1do+1di \frac{1}{f} = (n-1) (\frac{1}{R_1}-\frac{1}{R_2})=\frac{1}{d_o}+\frac{1}{d_i}
(n−1)(1−R−1−2R)=12R+1di(n−1)(1−R−1−2R)=12R+1di (n-1)(\frac{1}{-R}-\frac{1}{-2R})=\frac{1}{2R}+\frac{1}{d_i}
n−1−2R=12R+1din−1−2R=12R+1di \frac{n-1}{-2R}=\frac{1}{2R}+\frac{1}{d_i}
di=n−2Rdi=n−2R d_i=\frac{n}{-2R}

It turned out that my attempt wasn't accurate from the start, as it deviates from the solution provided. I couldn't understand how the first equation is formed in the solution.
Kaan99 said:
Hello,
This question is from 1990 Turkey National Physics Olympics. I tried my best to translate it clearly.
i think you have a very thick lens system so your thin lens formula will not work.
search in the textbook for thick lens formula.
 

Related to Image of an Object Inside Hollow Glass Sphere

1. What causes the image to appear inside a hollow glass sphere?

The image inside a hollow glass sphere is caused by the phenomenon of refraction. When light enters the sphere, it bends as it passes through the different mediums of air and glass, creating an image on the opposite side.

2. Why does the image appear upside down when viewed from the opposite side of the sphere?

The image inside a hollow glass sphere appears upside down because of the way light rays are refracted. The top of the image is created by the bottom of the object, and vice versa, due to the bending of light as it passes through the curved surface of the glass.

3. Does the size of the image change when viewed from different angles?

Yes, the size of the image inside a hollow glass sphere can change when viewed from different angles. This is due to the varying amount of refraction that occurs as the light passes through the curved glass surface.

4. What happens to the image if the glass sphere is filled with a different liquid?

If the glass sphere is filled with a different liquid, such as water or oil, the image will change due to the different refractive index of the liquid. This can result in a distorted or magnified image.

5. Can the image inside a hollow glass sphere be projected onto a screen?

Yes, the image inside a hollow glass sphere can be projected onto a screen by using a concave lens. The lens will reverse the upside-down image and project it onto the screen, creating a right-side-up image of the object inside the sphere.

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