Question

The left end of a long glass rod 8.60 cm in diameter, with an index of refraction 1.55, is ground and polished to a convex hemispherical surface with a radius of 4.30 cm . An object in the form of an arrow 1.53 mm tall, at right angles to the axis of the rod, is located on the axis 23.5 cm to the left of the vertex of the convex surface.

Find the height of the image of the arrow formed by paraxial rays incident on the convex surface.

Answer 1

The sign rules for the variables in the equation:

1. Sign rule for the object distance (s): when the object is on the same side of the refracting surface as the incoming light, object distances is positive otherwise, it is negative,

2. Sigu rule for the image distance (s dash): When the image is on the same side of the refracting Surface as the outgoing light (the refracted light), image distance is positive; otherwise, it is negative.

3. Sign rule for the radius of curvature of a spherical surface (R): When the center of curvature is on the same side as the outgoing light (the refracted light), the radius of curvature is positive otherwise, it is negative,

Apply: the above equation gives is the position of an image formed by refraction of light between a spherical interface of two different mediums.

To obtain this position, we need to get the radius of the spherical interface and the two refractive indexes of the mediums and the object position.

Note that we can use this formula for a plane interface when we put R equals to infinity as if the line of interface is considered a part of a sphere which has a radius of infinity.