Optics Experiment involving transmission through a gel and a sphere

[blizzardof96]

Assume you have the following scenario:

Light begins traveling through a gel of index of refraction n=1.34 in a straight line along the x axis. It is then incident on a solid sphere(n=1.36) of radius R in 3-space. Upon transmittance, the light again travels through the gel(n=1.36) and finally back into air(planar boundary) where it is incident on a detector.

Is it safe to assume that the further light is from the centre of the sphere, the longer it will take for light to hit the detector(due to spherical aberration)? My assumption is that due to spherical aberration, refraction is greater at the edge of the sphere and the light therefore travels a longer distance. By d=vt, it would also imply a greater amount of time before hitting the detector. My intuition suggests that light incident on the centre of the sphere will not refract(theta=0) and therefore takes path of least time(a straight line). Are these assumptions correct?

 

[tech99]

I am assuming that the light passes through the sphere, which is transparent.
I thought the operation of a dielectric lens was that rays near the centre are delayed relative to the edge. The spherical aberration is perhaps just a small error in the basic operation.
I also notice that the gel seems to weaken the focussing action greatly, and with the very long focal length then obtaining, I think spherical aberration will be small.
I presume the detector is placed at the focal distance.

 

[blizzardof96]

I am assuming that the light passes through the sphere, which is transparent.
I thought the operation of a dielectric lens was that rays near the centre are delayed relative to the edge. The spherical aberration is perhaps just a small error in the basic operation.
I also notice that the gel seems to weaken the focussing action greatly, and with the very long focal length then obtaining, I think spherical aberration will be small.
I presume the detector is placed at the focal distance.

You are correct about the focal length. I calculated it to be 68R suggesting a weaker focusing action. Can you explain why you believe that rays near the centre are delayed relative to the edge?

 

[tech99]

You are correct about the focal length. I calculated it to be 68R suggesting a weaker focusing action. Can you explain why you believe that rays near the centre are delayed relative to the edge?

Consider the case of a thin dielectric lens and let's take the case where there is a point source at its focus. We know that in geometrical optics the lens will form a parallel beam. To do this, the lens synthesizes an equi-phase wavefront across its aperture. A ray traveling via the edge of the lens is delayed by the extra distance travelled, so that a ray passing through the centre must be delayed by the dielectric by the same amount.
To return to the original question, I suppose that if the detector is placed at the focus, then (excluding spherical aberration), all ray paths have the same delay. The question is perhaps, where do we place the detector when we have strong aberration?

 

[blizzardof96]

Consider the case of a thin dielectric lens and let's take the case where there is a point source at its focus. We know that in geometrical optics the lens will form a parallel beam. To do this, the lens synthesizes an equi-phase wavefront across its aperture. A ray traveling via the edge of the lens is delayed by the extra distance travelled, so that a ray passing through the centre must be delayed by the dielectric by the same amount.
To return to the original question, I suppose that if the detector is placed at the focus, then (excluding spherical aberration), all ray paths have the same delay. The question is perhaps, where do we place the detector when we have strong aberration?

Okay, that is interesting. Assuming we place the detector at a position before the focal point and spherical aberration is essentially negligible(as you mentioned), would the intensity of the light on the detector(from different rays) be inversely proportional to path length within the solid sphere?