when a transparent vessel is is filled with water and a jet flows out of the vessel with a light source placed so that a horizontal beam enters the liquid jet. Under what conditions does the jet operate like a light candle?
By "light candle" I assume you mean "light pipe". Maybe I am using a more old-fashioned term for it.
The incidence angle of the light hitting the walls of the jet from the inside must be greater than the "critical" angle for total reflection, sin^-1 (1/1.33), which is 49 degrees.
To determine under what conditions the water jet will operate like a "light candle," we need to consider the phenomenon of total internal reflection. Total internal reflection occurs when light traveling through a medium encounters a boundary with a different medium at an angle greater than the critical angle, causing all the light to reflect back into the original medium.
In this case, the water jet can act like a light candle if total internal reflection takes place within the jet. For this to happen, the following conditions must be met:
1. The water jet must have a higher refractive index than the surrounding medium. In this case, since the water is flowing through a transparent vessel, the refractive index of the surrounding medium (air) remains constant, which is approximately 1. Therefore, the refractive index of the water should be higher than 1.
2. The angle of incidence of the light beam entering the water jet should be greater than the critical angle. The critical angle is determined by the refractive indices of both mediums involved. To calculate the critical angle, you will need to know the refractive index of water.
The formula to calculate the critical angle is:
Critical angle = sin^(-1) (n₂/n₁),
where n₁ is the refractive index of the medium where the light is coming from (air, approximately 1), and n₂ is the refractive index of the medium the light is entering (water).
Once you have determined the critical angle, the angle of incidence of the light beam entering the water jet should be greater than the critical angle for total internal reflection to occur. When this happens, the light within the water jet will be trapped and travel along the jet instead of refracting out, giving it the appearance of a "light candle."
Keep in mind that the refractive index of water depends on various factors such as temperature and impurities. So, you will need to refer to tables or measurements specific to the conditions of the water being used.