The maximum radiations from two bodies correspond to 560 nm and 420 nm respectively. The ratio of their temperature is:

Options

A. `4 : 3`
B. `3 : 4`
C. `2 : 1`
D. `3 : 2`

Explanation

To find the ratio of the temperatures of two bodies based on their maximum radiation wavelengths, we can use Wien's Displacement Law. This law states that the product of the wavelength at which the emission is maximum (λm) and the absolute temperature (T) of the black body is a constant (B).

The formula can be expressed as:
\[ \lambda_m \cdot T = B \]

From this, we can derive the relationship between the temperatures of two bodies based on their maximum radiation wavelengths:
\[ T \propto \frac{1}{\lambda_m} \]

This means that the temperature is inversely proportional to the wavelength. Therefore, if we have two bodies with maximum radiation wavelengths \( \lambda_1 \) and \( \lambda_2 \), their temperatures \( T_1 \) and \( T_2 \) can be expressed as:
\[ \frac{T_1}{T_2} = \frac{\lambda_2}{\lambda_1} \]

### Step-by-Step Solution:

1. **Identify the given wavelengths**:
- For body 1, \( \lambda_1 = 560 \, \text{nm} \)
- For body 2, \( \lambda_2 = 420 \, \text{nm} \)

2. **Set up the ratio of temperatures using Wien's Law**:
\[ \frac{T_1}{T_2} = \frac{\lambda_2}{\lambda_1} \]

3. **Substitute the values of the wavelengths**:
\[ \frac{T_1}{T_2} = \frac{420 \, \text{nm}}{560 \, \text{nm}} \]

4. **Simplify the ratio**:
\[ \frac{T_1}{T_2} = \frac{420}{560} = \frac{3}{4} \]

5. **Express the ratio in standard form**:
\[ T_1 : T_2 = 3 : 4 \]

### Final Answer:
The ratio of their temperatures \( T_1 : T_2 \) is \( 3 : 4 \).