Physics Q42 – JEE-MAIN 2025

A monochromatic light of frequency

5 \times 10^{14}

Hz travelling through air, is incident on a medium of refractive index '2'. Wavelength of the refracted light will be :

Clue 1 of 3: Fundamental Principle

Remember that the frequency of light remains constant when it passes from one medium to another, but its speed and wavelength change.

🥷

Ninja Strategy•Refractive Index Effect

First, calculate the wavelength in air. Then, recall that the wavelength in a medium is the wavelength in air divided by the refractive index of the medium.

🧠 Full Solution Path

Step 1: Calculate Wavelength in Air✦ Active

The speed of light in air (or vacuum) is $c = 3 \times 10^{8} m/s$ . The frequency of light is given as $f = 5 \times 10^{14} Hz$ . The wavelength in air ( $λ_{a}$ ) can be calculated using the formula $c = f λ_{a}$ .

λ_{a} = \frac{c}{f} = \frac{3 \times 10^{8} m/s}{5 \times 10^{14} Hz} = 0.6 \times 10^{- 6} m = 600 \times 10^{- 9} m = 600 nm

Step 2: Relate Wavelengths via Refractive Index○ Expand

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 ( $v$ ). It can also be expressed as the ratio of the wavelength in air ( $λ_{a}$ ) to the wavelength in the medium ( $λ_{m}$ ), since the frequency ( $f$ ) remains constant.

n = \frac{c}{v} = \frac{f λ_{a}}{f λ_{m}} = \frac{λ_{a}}{λ_{m}}

Step 3: Calculate Wavelength in Medium○ Expand

Given the refractive index $n = 2$ and the calculated wavelength in air $λ_{a} = 600 nm$ , we can find the wavelength in the medium ( $λ_{m}$ ).

λ_{m} = \frac{λ_{a}}{n} = \frac{600 nm}{2} = 300 nm

💡 Teacher's Secret Hint

Ensure units are consistent throughout the calculation, converting to nanometers at the end for the options.

✦ STEM Console utilizes AI models to generate step-by-step explanations and math clues. AI can make mistakes.

Physics Question 42 – JEE-MAIN 2025

Clue 1 of 3: Fundamental Principle

🧠 Full Solution Path