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: Understanding the Question:
Light of a fixed frequency enters a liquid. We know the wavelength inside the liquid. We must find the refractive index.

Step 2: Key Formula or Approach:
Frequency does not change when light enters a new medium. Speed in the medium is \(v = f\lambda\). The refractive index is \(n = c/v\).

Step 3: Find the Speed in the Liquid:
\[ v = f\lambda = 5 \times 10^{14} \times 450 \times 10^{-9} = 2.25 \times 10^{8}\ \text{m/s} \]

Step 4: Find n:
\[ n = \frac{c}{v} = \frac{3 \times 10^{8}}{2.25 \times 10^{8}} = 1.33 \]

Step 5: Checking Each Option:
1.25, 1.45 and 1.51 do not match 1.33. Option 2 is correct.

Final Answer:
The refractive index of the liquid is 1.33, so option 2 is correct. \[ \boxed{n = 1.33} \]