Relative refractive index of two media is 0.80. In one of them, light has wavelength $6000\text{A°}$ and travels at $\text{2}{\text{.4×10}}^8\text{m/s}$ . This light is refracted into the second medium. Its frequency in the second medium is

The problem states that the relative refractive index between two media is 0.80. The light has a wavelength of 6000 Å in the first medium and travels at a speed of 2.4 × 10⁸ m/s. We are asked to find the frequency of the light in the second medium after it undergoes refraction.

Step 1: Convert the Given Values

We are given the following information:

• Wavelength in the first medium, λ₁ = 6000 Å
• Speed of light in the first medium, v₁ = 2.4 × 10⁸ m/s
• Relative refractive index, n₁₂ = 0.80

To proceed, we first convert the wavelength from Ångströms (Å) to meters:

1 Å = 10^-10 meters, so:

λ₁ = 6000 Å = 6000 × 10^-10 m = 6 × 10^-7 m

Step 2: Calculate the Frequency in the First Medium

The frequency of light is related to the wavelength and velocity of the wave by the equation:

v = λ × f

Where v is the velocity, λ is the wavelength, and f is the frequency.

To calculate the frequency f₁ in the first medium:

f₁ = v₁ / λ₁

Substitute the values:

f₁ = (2.4 × 10⁸ m/s) / (6 × 10^-7 m) = 4 × 10¹⁴ Hz

Step 3: Frequency Remains Constant During Refraction

According to the principle of refraction, the frequency of light remains constant as it passes from one medium to another. Thus, the frequency in the second medium, f₂, will be the same as the frequency in the first medium, f₁.

Therefore, f₂ = f₁ = 4 × 10¹⁴ Hz.

Step 4: Apply the Relative Refractive Index

Now, using the relative refractive index, we can calculate the velocity of light in the second medium. The relative refractive index n₁₂ is defined as:

n₁₂ = v₁ / v₂

Rearranging this equation gives us the velocity of light in the second medium:

v₂ = v₁ / n₁₂

Substitute the given values:

v₂ = (2.4 × 10⁸ m/s) / 0.80 = 3.0 × 10⁸ m/s

Step 5: Conclusion

The frequency of the light in the second medium remains unchanged, as expected due to the principle of frequency conservation during refraction. Thus, the frequency in the second medium is:

f₂ = 4 × 10¹⁴ Hz

In conclusion, while the wavelength and speed of light change when transitioning between media with different refractive indices, the frequency remains constant. This is a key property when studying the behavior of light in different mediums, and the relative refractive index plays a critical role in determining how these properties change.