89 views

### Fermat's principle of least time for reflection and refraction [duplicate]

In discussing geometrical optics, Fermat's principle of least time is often used to solve problems and is generally used as a replacement of laws of reflection and refraction. Fermat's principle is ...
6k views

### Can you explain Fermat's Principle to me?

The textbook(F.A.Jenkins and H.E.White Fundamentals of Optics) states that the Fermat's principle is that the path taken by a light ray in going from one point to another through any set of media ...
• 499
2k views

### Another Solution To Brachistochrone Problem

Recalling the statement of the problem : Given two points A and B in a vertical plane, what is the curve traced out by a point acted on only by gravity, which starts at A and reaches B in the ...
• 11.4k
2k views

### Determining the path of a light ray

Let's consider a ray in the plane $xy$. Let the refractive index be defined in any point of the plane with the function $n(x,y)$. In time $t=0$ the ray is located in coordinates $(x_0, y_0)$ and its ...
• 557
1k views

Why when deriving the law of reflection from Fermat's principle of least time do I set $dL/dx = 0$? I am a 12 grade student with a little notions of maxima and mimima in one variable calculus.
• 103
330 views

### Why does Fermat's principle (optics) not apply to all paths?

Feynman's statement of Fermat's Principle regarding optics is the following, "a ray going in a certain particular path has the property that if we make a small change (say a one percent shift) in ...
300 views

### Refraction across two interfaces: is it correct to use Snell's law as constraint in an application of Fermat's principle?

The problem area is geometric optics, namely refraction across homogeneous media with constant speed of light. I explain the three steps of a methodological doubt that popped up. Polite request: ...
• 151
978 views

### Snell's law and Fermat's principle

I have read this sentence on a book about the Snell's law of refraction, referring on a ray that passes from air ($n_1=1$) to glass ($n_2=1.55$): "Snell's equation can be derived from Fermat's ...
• 1,207
2k views

### Equations of Fermat's principle/Snell's law in a gradient lens (sugar aquarium)

I'm trying to animate a beam of light inside a substance with gradient index of refraction as a function of y. A good example of that is a syrup inside an aquarium like here https://www.youtube.com/...
• 59
1 vote
2k views

### Why does light bend towards the normal when passing through a denser medium?

When light passes from a medium with less refractive index to a medium with higher refractive index, it bends towards the normal. But why normal . Of course we can take an example of a car moving from ...
2k views

### Deriving Snell's Law from Fermat's Principle, why do we differentiate only with respect to $x$?

I'm confused about why we only differentiate with respect to the X when deriving Snell's law. Can someone explain why we do not also do a differentiation with respect to Y. For more clarification ...
1 vote
838 views

### Fermat's principle

The actual ray path between two points is the one for which the optical path length is stationary with respect to variations of the path. Can you explain me what is extremum path?
1 vote
511 views

### Refraction of light rays

My textbook says that the greater the refractive index of a medium, the lower the speed of a light ray passing through it. Seawater has a slightly larger refractive index than fresh water. Light ray ...
428 views

### Derivation of relationship between speed of light in two mediums and the angle of refraction and incidence

I came across the following equation for the speed of light in different medium and the angle of reflection(Θ1) and refraction(Θ2): sin(Θ1)/sin(Θ2)=v1/v2=constant My textbook does not give any ...
• 443
My book states it as $(\sin i)/(\sin r)=n$. However, University Physics has a different say. It says, $n_{a} \sin a =n_{b} \sin b$. Which of the following is correct?