A monochromatic light of wavelength 6000A in vacuum enters a medium of refractive index 1.5.The wavelength of it in this medium is

To find the wavelength of monochromatic light in a medium with a refractive index, we can use a straightforward relationship between the wavelength in vacuum and the wavelength in the medium. The refractive index (n) of a medium is defined as the ratio of the speed of light in vacuum (c) to the speed of light in the medium (v). This relationship can also be expressed in terms of wavelength.

Understanding the Relationship

The formula that connects the wavelength in vacuum (λ₀) to the wavelength in a medium (λ) is given by:

• λ = λ₀ / n

Where:

• λ is the wavelength in the medium.
• λ₀ is the wavelength in vacuum.
• n is the refractive index of the medium.

Applying the Values

In your case, the wavelength of the light in vacuum is given as 6000 Å (angstroms), which is equivalent to 6000 x 10^-10 meters. The refractive index of the medium is 1.5. Now, we can substitute these values into the formula:

• λ = 6000 Å / 1.5

Calculating the Wavelength

Now, let's perform the calculation:

• λ = 6000 Å / 1.5 = 4000 Å

Thus, the wavelength of the light in the medium with a refractive index of 1.5 is 4000 Å.

Visualizing the Concept

To visualize this, think of light as a wave traveling through different mediums. In vacuum, it travels faster and has a longer wavelength. When it enters a medium like glass or water, it slows down, which results in a shorter wavelength. This is similar to how a car slows down when it enters a crowded street, making it cover less distance in the same amount of time.

Final Thoughts

Understanding how light behaves in different mediums is crucial in fields like optics and photography, where the manipulation of light can lead to various effects. The calculation we performed shows how the properties of light change based on the medium it travels through, which is fundamental in many scientific applications.