**Wavelength of Light in Diamond**

To calculate the wavelength of light in diamond, we need to use the concept of Snell's law, which relates the angles of incidence and refraction to the refractive indices of the two media involved. Snell's law can be expressed as:

n1 * sin(θ1) = n2 * sin(θ2)

Where:
- n1 is the refractive index of the medium the light is coming from (in this case, vacuum)
- θ1 is the angle of incidence
- n2 is the refractive index of the medium the light is entering (in this case, diamond)
- θ2 is the angle of refraction

In this problem, the light is passing from vacuum (n1 = 1) into diamond (n2 = 2.4). Since the problem does not provide an angle of incidence, we assume that the light is incident normally, meaning the angle of incidence is 0 degrees. Therefore, sin(θ1) = 0, and sin(θ2) = 0 as well.

This allows us to simplify Snell's law to:

n1 * sin(θ1) = n2 * sin(θ2)
1 * 0 = 2.4 * 0

Since both sides of the equation are zero, this equation is true. Therefore, the angle of refraction, θ2, can be any value.

Given that the wavelength of light in vacuum is 500 nm, we can use the formula:

λ2 = λ1 / n2

Where:
- λ2 is the wavelength of light in the diamond
- λ1 is the wavelength of light in vacuum

Substituting the values, we get:

λ2 = 500 nm / 2.4

Calculating this, we find:

λ2 ≈ 208.33 nm

Therefore, the wavelength of light in diamond is approximately 208.33 nm.

**Explanation:**

When light passes from one medium to another, its speed and direction change due to the change in refractive index. The refractive index is a measure of how much the speed of light is reduced in a medium compared to vacuum. In this case, the refractive index of diamond is 2.4, meaning light travels 2.4 times slower in diamond than in vacuum.

As a result, the wavelength of light in diamond is shorter than in vacuum. This phenomenon is known as wavelength reduction or wavelength shift. In the given problem, the wavelength of light in diamond is reduced to approximately 208.33 nm from its original value of 500 nm in vacuum.

It is important to note that the refractive index of a material is dependent on the wavelength of light. Different wavelengths will experience different amounts of refraction when passing through a medium. This phenomenon is responsible for the dispersion of white light into its constituent colors when passing through a prism.

In conclusion, the wavelength of light in diamond is shorter than in vacuum due to the difference in refractive index between the two media.

Speed = Wavelength x Frequency=> 3 x 108 = 500 x 10-9 x Frequency. (For vacuum)=> Frequency = 3 x 108 /500 x 10-9In any medium the frequency of light remains constantSpeed = Wavelength x Frequency=>3 x 108/2.4 = Wavelength x (3 x 108 )/ 500 x 10-9=> Wavelength = 500x 10-9/2.4 = 208.33 nm.