What must the critical angle be if light transmits from diamond into water?

To determine the critical angle for light transmitting from diamond into water, we need to understand a concept called Snell's law.

Snell's law states that the angle of incidence (the angle at which light rays strike a boundary between two mediums) is related to the angle of refraction (the angle at which light rays bend as they pass from one medium to another), and the refractive indices of the two mediums.

The refractive index is a measure of how much a medium slows down light compared to its speed in a vacuum. For diamond, the refractive index is approximately 2.42, and for water, it is approximately 1.33.

The critical angle occurs when the angle of refraction becomes 90 degrees. Any angle of incidence greater than the critical angle will result in total internal reflection, meaning that all the light is reflected back into the diamond instead of being transmitted into the water.

The formula to calculate the critical angle is:

Critical angle = sin^(-1)(n2/n1)

Where:
- n1 is the refractive index of the medium the light is coming from (in this case, diamond),
- n2 is the refractive index of the medium the light is entering (in this case, water),
- sin^(-1) is the inverse sine function that gives us the angle in radians, and we can convert it to degrees if needed.

Substituting the values, we get:

Critical angle = sin^(-1)(1.33/2.42)

Using a scientific calculator, we can find that the critical angle is approximately 38.81 degrees. So, for light to transmit from diamond into water, the angle of incidence must be less than 38.81 degrees.