Semi circular prism and light rays

[hallowon]

Homework Statement

So anyway in the diagram of my book there is a ray hitting the centre in the flat part of a semi circular prism. The question in the book states "Ignoring partial reflection, we know that each ray will pass through the flat surface and then pass through the curved surface, Which of the rays refract only once? Explain" I also do not get why it refracts more than once if the light rays do not hit the centre.

Homework Equations

Snell's law

The Attempt at a Solution

I know from the centre to the edge it is the radius of the semi circular prism. When the light refracts from the centre onto the edge i know that the normal is perpendicular to that point and the angle of refraction = 0.

 

[Redbelly98]

Homework Statement

So anyway in the diagram of my book there is a ray hitting the centre in the flat part of a semi circular prism. The question in the book states "Ignoring partial reflection, we know that each ray will pass through the flat surface and then pass through the curved surface, Which of the rays refract only once? Explain" I also do not get why it refracts more than once if the light rays do not hit the centre.

Homework Equations

Snell's law

The Attempt at a Solution

I know from the centre to the edge it is the radius of the semi circular prism. When the light refracts from the centre onto the edge i know that the normal is perpendicular to that point and the angle of refraction = 0.

Welcome to PF

Something is not clear from what you wrote. Is there just a single ray in the figure, hitting the center of the flat side? Or are there more rays (and if yes, please describe their path, i.e. where and at what angle are they incident on the prism?)

It sounds like they are defining "to refract" as "to pass through a surface and exit at an angle different than the incident angle". In other words, if a ray passes through a surface without changing its angle, it is not considered to refract there.

If so, you'll need to think about under what condition a ray does not change its angle when passing through a surface.

 

[thomate1]

This means that the light ray will not refract at the edge and will continue in a straight line.

However, when the light ray hits the flat surface, it will refract according to Snell's law as it enters a different medium. This means that it will bend towards the normal, and when it reaches the curved surface, it will again bend towards the normal as it enters a different medium. This second refraction is what causes the light ray to refract more than once in the semi circular prism.

To determine which rays refract only once, we need to consider the angle at which the ray enters the flat surface. If the angle of incidence is equal to the critical angle, then the ray will undergo total internal reflection and will not refract at the curved surface. This means that it will only refract once, at the flat surface.

On the other hand, if the angle of incidence is less than the critical angle, the ray will refract at both the flat and curved surfaces, resulting in more than one refraction. This is why some rays refract more than once in the semi circular prism.