Refraction at spherical surface

[desmond iking]

Homework Statement

A semi-circle shaped cylindrical glass block has a radius of curvature of 10.0cm. and a refractive index of 1.50 as shown. A pin is placed at the centre of curvature O . How far from the surface do the pin appear to be when it is viewed along the axis of the spherical surface?

Homework Equations

The Attempt at a Solution

The diagram is in the photo and the solution is in the photo , p/s : this is the notes from my senior.
from the digram , I know that the object is placed on the left , whereas the refracting surface is concave relative to the the object . (assume the light pass from left to right). in the photo 2 , i was told that if refracting surface is concave relative to the the object , then the radius of curvature is negative... but here, the notes give the radius of curvature is positive. which on is correct? can someone help please?

 

[HallsofIvy]

Pick several points on the surface of the sphere and consider rays from tip of the pin to each point. Use the tangent plane at each point to determine the path of the ray within the sphere. If they all intersect at a single point that is the image of the tip of the pin. If they do not intersect at a single point, there is no image. Do the same for the other end of the pin.

 

[desmond iking]

Pick several points on the surface of the sphere and consider rays from tip of the pin to each point. Use the tangent plane at each point to determine the path of the ray within the sphere. If they all intersect at a single point that is the image of the tip of the pin. If they do not intersect at a single point, there is no image. Do the same for the other end of the pin.

which on is correct? the radius of curvature is positive or negative?