Question

A ray of light of frequency \(5 \times 10^{14}\) Hz is passed through a liquid. The wavelength of light measured inside the liquid is found to be \(450 \times 10^{-9}\) m. The refractive index of the liquid is

• A. 1.25
• B. 1.33
• C. 1.45
• D. 1.51

Hint:

Use \(n = c/(f\lambda)\). Frequency does not change in the liquid.

Answer 1

The Correct Option is B

Step 1: Find the Wavelength in Vacuum:
In vacuum, $\lambda_0 = c/f = (3 \times 10^{8})/(5 \times 10^{14}) = 6 \times 10^{-7}$ m, which is 600 nm.

Step 2: Use the Wavelength Ratio:
The refractive index also equals the ratio of the wavelength in vacuum to the wavelength in the medium, since frequency stays the same: $n = \lambda_0/\lambda$.

Step 3: Calculate:
\[ n = \frac{600\ \text{nm}}{450\ \text{nm}} = \frac{4}{3} \approx 1.33 \] This is the value for water.

Step 4: Pick the Option:
1.33 is the second printed option.

Final Answer:
\[\boxed{n = 1.33\ \text{(option 2)}}\]