Using idea of wave fronts why does a light ray bend upon enterin a slower medium @ a nonzero angle of incidenc

Question

also why will it not bend when the angle of incidence is zero?

Answer 1

1. You first have to understand why light travels in a straight line in a UNIFORM medium!

Think of lots of individual point sources situated along the wave front. Now imagine new subsidiary waves, all radiating out from each source into the medium into which the original wave was advancing, at speed ' cm,' where ' cm ' is the speed of light in the medium ' m.'

After a set, short standard amount of time ' t,' these new subsidiary waves will all form overlapping circles of radius (cm t). The furthest advanced fronts will closely overlap, and the denser the distribution of the sources along the original front, the more the advanced parts of the overlapping circles will represent the entire wave-front, as a whole, having advanced by a distance (cm t) PERPENDICULAR to the original wave-front.

The DIRECTION of propagation is PERPENDICULAR to the NEW wavefront, while the latter is parallel to the OLD wavefront.

And THAT'S why light travels in a straight line in a uniform medium.

Good. Now that we've got the classical propagtion of light (literally!) straight, we can move on to curved or bent paths.

2. Now imagine what happens if the velocity of propagation becomes smaller, either gradually or precipitously, on some part of the wavefront, at one side of a finite section of wavefront, say, while remaining unaltered on the other part of it. . Then while the wavefront advances the SAME DISTANCE [we'll now call it (c1 t) in the original, undisturbed medim 1] everywhere that nothing has changed, it will advance LESS DISTANCE, (c2 t), where its new velocity c2 is less than c1.

It's best to first consider a given, constant jump down in wave speed that occurs along a line y = 0, say, with light approaching that from the side y > 0 at an oblique angle.

The consequence is best appreciated by making a little diagram, showing how the new wave fronts in the "reduced speed" medium now overlap and line up. You should see that the wave-front in the new medium (in the region y < or equal to 0), by successively travelling less distance than in the original medium, will result in that part of the wave having been retarded and therefore "bent" in its progress through the new medium. Therefore, it now represents a wave travelling closer to the perpendicular (or norma)l to the interface between the two media.

In other words, it's been "refracted" towards the normal.

3. In a medium where the change in speed on one side of some slab of wavefront is continuous, rather than discontinuous, the following will happen. Adjacent portions of the wavefront, going towards the slower moving end, will gradually curve more and more away from the original direction. The effect will be some sideways dispersal of the wave as the original "normals" now diverge from one another. As a whole, the now CURVED wave-front will still be changing its form in such a way that the rays are bending more and more into the slower medium.

4. When the angle of incidence is zero, the initial wavefront is advancing into the slower medium EQUALLY at all points on the wavefront. All the "slow-down" factors will now be the same, at ALL points on the wavefront. So the wavefront still advances by the same amount everywhere along it, even IF that new distance of aqdvancement in time ' t ' (c2 t) is now LESS that it would have been (c1 t) in the original medium.

Hence, not only is there NO REASON for the light to change its direction of motion, it DOESN'T change that direction.

Another way to reach this same answer is also possible, if you think about it. Here is a situation of complete symmetry and equivalence, at EVERY POINT on the wave-front. That being so, how on Earth could you ever identify some PARTICULAR direction in which the wavefront and/or the light's path is going to be bent or deviated? That requires the physical identification of a special direction, that special direction being identifiable at all of the different points on the waverfont.

But in the physical situation you have envisaged, THERE IS NO SUCH SPECIAL DIRECTION, and therefore the angle of propagation CANNOT change. All that can change is that the distance actually travelled in a given time will reflect the reduced speed of light on the wavefront; its direction of travel remains unaltered.

I believe that I have now answered your questions.

Live long and prosper.

Answer 2

interior the universe there are 4 sorts of forces, reliable nuclear, vulnerable nuclear, electromagnetic, and gravity... the two nuclear forces are the main effective forces interior the universe however their variety is constrained to the atomic and subatomic ranges, then electromagnetic and then the weakest rigidity is gravity. even however easy has no mass it continues to affix the universe, and it somewhat is effected by using the forces that lie interior, specifically gravity. for occasion, in black holes the gravity is so large that easy can not get away (which grants a medium wherein easy slows down and thus it surely stops all jointly).