A red colour in air has wavelength 760 nm when light passes through water of refractive index `(n=4/3)`, wavelength becomes 570 nm. (wavelength of yellow colour in air is 570 nm). Then colour of red light in water is

Options

A. Red
B. Green
C. Yellow
D. Blue

Answer

To determine the color of red light in water, we need to analyze the information given in the question step by step.

### Step 1: Understand the relationship between wavelength, frequency, and refractive index
The speed of light in a medium is given by the equation:
\[ v = f \cdot \lambda \]
where:
- \( v \) is the speed of light in the medium,
- \( f \) is the frequency of light,
- \( \lambda \) is the wavelength of light in that medium.

When light travels from one medium to another, its frequency remains constant, while its speed and wavelength change.

### Step 2: Calculate the wavelength of red light in water
Given:
- Wavelength of red light in air (\( \lambda_1 \)) = 760 nm
- Refractive index of water (\( n \)) = \( \frac{4}{3} \)

The relationship between the wavelengths in different media is given by:
\[ \lambda_2 = \frac{\lambda_1}{n} \]
where:
- \( \lambda_2 \) is the wavelength in the new medium (water),
- \( n \) is the refractive index of the new medium.

Substituting the values:
\[ \lambda_2 = \frac{760 \, \text{nm}}{\frac{4}{3}} \]
\[ \lambda_2 = 760 \, \text{nm} \times \frac{3}{4} \]
\[ \lambda_2 = 570 \, \text{nm} \]

### Step 3: Identify the color corresponding to the new wavelength
We know that:
- The wavelength of yellow light in air is 570 nm.

Since the wavelength of red light in water is calculated to be 570 nm, which corresponds to yellow light, we can conclude that:

**The color of red light in water will appear yellow.**

### Final Answer
The color of red light in water is yellow.

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