Understanding Light Refraction from Air to Water

When light travels from one medium to another, it changes direction. This phenomenon is called refraction of light.

Let's define some important terms related to refraction:

• Angle of incidence: The angle between the incident ray (the light ray hitting the boundary between the two media) and the normal (an imaginary line perpendicular to the boundary surface at the point of incidence).
• Angle of refraction: The angle between the refracted ray (the light ray after passing into the second medium) and the normal in the second medium.
• Normal: An imaginary line drawn perpendicular to the surface at the point where the light ray strikes it.

The bending of light depends on the optical density of the two media. Air is considered an optically rarer medium compared to water, which is an optically denser medium. The speed of light is higher in a rarer medium (like air) and lower in a denser medium (like water).

When light passes from an optically rarer medium (air) to an optically denser medium (water), the speed of light decreases. This decrease in speed causes the light ray to bend towards the normal.

If the light ray bends towards the normal, the angle it makes with the normal in the second medium (angle of refraction) will be smaller than the angle it made with the normal in the first medium (angle of incidence).

This behavior is described by Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media:

\( \frac{\sin{\theta_1}}{\sin{\theta_2}} = \frac{v_1}{v_2} = \frac{n_2}{n_1} \)

Where:

• \( \theta_1 \) is the angle of incidence in the first medium (air).
• \( \theta_2 \) is the angle of refraction in the second medium (water).
• \( v_1 \) is the speed of light in the first medium (air).
• \( v_2 \) is the speed of light in the second medium (water).
• \( n_1 \) is the refractive index of the first medium (air).
• \( n_2 \) is the refractive index of the second medium (water).

Since water is denser than air, its refractive index (\( n_{water} \)) is greater than the refractive index of air (\( n_{air} \)). So, \( n_{water} > n_{air} \). From Snell's Law (\( n_{air} \sin{\theta_{air}} = n_{water} \sin{\theta_{water}} \)), if \( n_{water} > n_{air} \), then \( \sin{\theta_{air}} > \sin{\theta_{water}} \). Since the sine function increases with angle in the range of possible angles of incidence and refraction (0° to 90°), this implies \( \theta_{air} > \theta_{water} \).

Therefore, when light passes from air to water, the angle of refraction is less than the angle of incidence.