Question

rays of light from the ray box will refract in what direction? explain using terms such as ray of incidence, ray of refraction, medium, refractive index.

Explanation:

Step1: Recall the law of refraction

When light travels from a medium with a lower refractive index (air, here considered as the medium from the ray - box) to a medium with a higher refractive index (liquid in the semicircular container), the ray of incidence bends towards the normal.
The ray of incidence is the incoming light ray from the ray - box. The ray of refraction is the light ray after it has entered the new medium (liquid). The refractive index ($n$) of a medium is a measure of how much the speed of light is reduced inside the medium compared to its speed in vacuum. Mathematically, the relationship between the angle of incidence ($\theta_{i}$) and the angle of refraction ($\theta_{r}$) is given by Snell's law: $n_1\sin\theta_{i}=n_2\sin\theta_{r}$, where $n_1$ is the refractive index of the first medium (lower refractive index, $n_1 < n_2$ if going from air - like to liquid - like medium) and $n_2$ is the refractive index of the second medium. Since $n_1 < n_2$, for a non - zero angle of incidence, $\sin\theta_{i}>\sin\theta_{r}$ (from Snell's law) and $\theta_{i}>\theta_{r}$ (because the sine function is increasing for angles between $0^{\circ}$ and $90^{\circ}$), so the ray bends towards the normal.

Answer:

The rays of light (ray of incidence) from the ray - box will bend towards the normal. When light moves from a medium with a lower refractive index (the medium from which the ray - box emits light, assume it has a refractive index $n_1$) to a medium (liquid in the semicircular container) with a higher refractive index ($n_2$, $n_2>n_1$), according to Snell's law ($n_1\sin\theta_{i}=n_2\sin\theta_{r}$), the angle of refraction ($\theta_{r}$) is smaller than the angle of incidence ($\theta_{i}$). So the ray of refraction bends towards the normal.