Suppose A light ray starts

at the point A = (0,a) in an uniform medium 1 where the speed of light is c1 and then passes through an uniform medium 2 where the speed of light is c2 reaching point B = (d, −b). The line separating the two media is the x-axis;

HINTS ONLY
1) what is the shortest path of the light ray from A to B
2) what time is needed for the light ray to travel along the first path - in medium 1
3) same thing as (2) part 2 path

try this discussion:

http://dev.physicslab.org/Document.aspx?doctype=3&filename=GeometricOptics_LeastTime.xml

To find the shortest path of the light ray from point A to point B, we need to minimize the time taken by the light ray to travel between the two points. This can be done using Fermat's principle, which states that light takes the path that minimizes the travel time.

1) The shortest path of the light ray from A to B can be found using the principle of least time. According to Fermat's principle, light should travel in a straight line in a uniform medium. Therefore, the shortest path will be a straight line between A and B, which happens to be a straight line along the x-axis.

2) To find the time needed for the light ray to travel along the first path in medium 1, we can use the formula:

time = distance / speed

The distance is the horizontal distance from A to B, which is d units. The speed of light in medium 1 is given as c1. Therefore, the time taken for the light ray to travel along the first path is:

time = d / c1

3) For the second part of the path in medium 2, we need to consider that the light ray will be refracted at the interface between medium 1 and medium 2, due to the change in the speed of light. To find the time needed for this second path, we need to use Snell's Law.

Snell's Law states that the ratio of the sines of the angles of incidence (θ1) and refraction (θ2) is equal to the ratio of the speeds of light in the two media. Therefore, we have:

sin(θ1) / sin(θ2) = c1 / c2

In this case, the light ray is incident normally on the interface between the two media, so the angle of incidence is 90 degrees (π/2 radians). Therefore, sin(θ1) = 1.

The angle of refraction can be found using Snell's Law:

sin(θ2) = (c2 / c1) * sin(θ1)

Since sin(θ1) = 1 in this case, we can simplify it to:

sin(θ2) = c2 / c1

The time taken for the second part of the path can be calculated using the formula:

time = distance / speed

The distance here is the vertical distance from point A to point B, which is -b units. The speed of light in medium 2 is given as c2. Therefore, the time taken for the light ray to travel along the second path is:

time = -b / c2

Remember to take the magnitude of the vertical distance (-b) before dividing it by the speed of light in medium 2 (c2).