Consider one point on an object near a lens.
a. What is the minimum number of rays needed to locate its image point? Explain.
b. How many rays from this point actually strike the lens and refract to the image point?
a. Two rays needed to locate its image point.
b. Infinite number of rays from this point actually strike the lens and refract to the image point .
In an optical system, a ray is the path along which light energy is conveyed from one point to another.
The laws of reflection and refraction are the categorical imperatives of geometrical optics. A light ray travels in a straight line if it is not reflected or refracted.
To identify the image point of a point object, precisely two rays are essential.
An enormous amount of rays from this point strike the lens and, after refracting through the lens, form a single point image.
Even though each light ray seems to have its own route, they all start at the same object point and end at the same image point.
Shows a light ray that travels from point A to point B. The ray crosses the boundary at position x, making angles and in the two media. Suppose that you did not know Snell’s law.
A. Write an expression for the time t it takes the light ray to travel from A to B. Your expression should be in terms of the distances a, b, and w; the variable x; and the indices of refraction n1 and n2
B. The time depends on x. There’s one value of x for which the light travels from A to B in the shortest possible time. We’ll call it . Write an expression (but don’t try to solve it!) from which could be found.
C. Now, by using the geometry of the figure, derive Snell’s law from your answer to part b.
You’ve proven that Snell’s law is equivalent to the statement that “light traveling between two points follows the path that requires the shortest time.” This interesting way of thinking about refraction is called Fermat’s principle.
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