A glass rod with a refractive index of 1.53 is ground and polishedat both ends to hemispherical surfaces with radii of 6.10 . When anobject is placed on the axis of the rod, a distance of 20.0 to theleft of the left-hand end, the final image is formed at a distanceof 69.0 to the right of the right-hand end.
What is the length of the rod measured between the vertexes of thetwo hemispherical surfaces?

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The left end of a long glass rod 8.00 ${\rm cm}$ in diameter and with an index of refraction of 1.60 is ground and polished to a convex hemispherical surface with a radius of 4.00 ${\rm cm}$ . An object in the form of an arrow 1.90 ${\rm mm}$ tall, at right angles to the axis of the rod, is located on the axis 23.0 ${\rm cm}$ to the left of the vertexof the convex surface.
Part A:
Find the position of the image of the arrow formed by paraxial rays incident on the convex surface.
Part B:
Find the height of the image formed by paraxial rays incident on the convex surface.

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The left-hand of a glass rod is ground to a spherical surface. Theglass has index of refraction 1.50. A small object 4.00 mm tall isplaced in the axis of the rod, 12.0 cm to the left of the vertex ofthe spherical surface. The image is formed in the rod, 19.0 cm tothe right of the vertex.

(a) What is the magnitude of the radius of curvature of thespherical surface at the end of the rod?

(b) What is the height of the image?

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A very thin glass rod 4 meters long is rubbed all over with a silkcloth. It gains a uniformly distributed charge 1.6X10^â6 C. Twosmall spherical rubber balloons of radius 1.2 cm are rubbed allover with wool. They each gain a uniformly distributed charge of-8X10^â8 C. The balloons are near the midpoint of the glass rod,with their centers 3 cm from the rod. The balloons are 2 cm apart(4.4 cm between centers).

(a) Find the net electric field at the location marked by the X,0.6 cm to the right of the center of the left balloon. Things tothink about: Which objects make nonzero contributions to E field atthis location? What are the correct distances from sources to theobservation location? What is the direction of E field due to therod? (The drawing is not to scale; read the problem statementcarefully. Assume the +x axis is to the right, the +y axis is up,and the +z axis is out.)

E = ________ N/C

(b) What approximations did you make, if any? Which apply(1-4)?
1. Neglect polarization of balloons.
2. Use approximate formula for electric field of a chargedspherical shell.
3. Neglect polarization of rod.
4. Assume distance to observation location is small compared tolength of rod.

(c) Next a proton is placed at that same location (marked by thex). What is the force acting on the proton?

F = ________ N

Note: in parts (a) and (c) there should be an arrow over the"E" and the "F" but the custom equation function would not workproperly.

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