# Question regarding Ray Optics and Probability

• Ayan Ghazi
In summary, the conversation discusses a problem involving a sphere with a perfectly reflecting inner surface and a hole that allows a ray of light to enter. The question is to find the angle made with the normal of the hole that results in the least probability of the ray coming out. The problem is simplified by considering two dimensions instead of three, but complicated by factors such as diffraction bending and the size of the hole.
Ayan Ghazi
Let there be a sphere whose inner surface consists of a perfectly reflecting surface.
It has a hole on it which allows a ray of light to enter.
Give the angle made with the normal of the hole when the ray of light enters such that the probability
that the ray comes out is the least?Assuming the ray can enter through any angle with the hole.
(eg.if the angle with the normal is 0 then probablity that the ray comes out is 1 as the ray reflects from the
surface and retraces itself resulting in the ray coming out in one reflection only)

Ayan Ghazi said:
Give the angle made with the normal of the hole when the ray of light enters such that the probability
that the ray comes out is the least?
Hi Ayan:

I think the problem is simpler with respect to one aspect, and more complicated with respect to other aspects, than it superficially seems.

The simplification is that the problem requires a solution in only two dimensions rather than three.

I am guessing that you assume the hole is circular. One complication is that the ray angle will be affected on entry by diffraction bending. The amount of bending depends on the size of the hole and the wave length distribution of of the photons in the ray. You may want to make an assumption (probably unrealistic) that there is no entry diffraction.

A second complication is that the size of the hole determines how close the center of the ray needs to be to the center of the hole in order for the ray to to escape.

Regards,
Buzz

## What is ray optics and how does it differ from wave optics?

Ray optics is a branch of optics that explains the behavior of light as it travels through transparent materials. It focuses on the geometric principles of light, such as reflection and refraction. In contrast, wave optics considers light as a wave and explains its behavior through concepts like interference and diffraction.

## What is the law of reflection and how is it applied in ray optics?

The law of reflection states that the angle of incidence is equal to the angle of reflection. In ray optics, this law is used to predict the path of light as it reflects off a surface. The incident ray, reflected ray, and normal (perpendicular line) at the point of reflection all lie on the same plane.

## What is Snell's law and how is it used in ray optics?

Snell's law, also known as the law of refraction, states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speeds of light in the two media. In ray optics, this law is used to predict the direction of the refracted ray as it passes through a boundary between two materials.

## What is the relationship between probability and optics?

In optics, probability is used to describe the likelihood of a photon interacting with a material or passing through a specific region. This is especially relevant in quantum optics, where the probabilistic nature of light is taken into account when studying its behavior.

## What is the role of probability in determining the behavior of light in multiple-slit interference experiments?

In multiple-slit interference experiments, probability is used to explain the patterns of light and dark fringes observed on a screen. The probability of a photon passing through a specific slit and interfering with other photons is dependent on the distance between the slits and the wavelength of light, resulting in the observed interference pattern.

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