A star is going away from the earth. An observer on the earth will see the wavelength of light coming from the star

Options

A. Decreased
B. Increased
C. Neither decreased nor increased
D. Decreased or increased depending upon the velocity of the star

Answer

To solve the problem of how an observer on Earth perceives the wavelength of light coming from a star that is moving away, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Doppler Effect**:
The Doppler effect describes how the frequency (and consequently the wavelength) of light changes for an observer moving relative to the source of the light. When a source of light is moving away from an observer, the observed frequency decreases.

**Hint**: Recall that the Doppler effect applies to all types of waves, including sound and light.

2. **Identify the Variables**:
- Let \( v \) be the actual frequency of the light emitted by the star.
- Let \( c \) be the speed of light.
- Let \( b \) be the speed of the star moving away from Earth.

3. **Apply the Doppler Effect Formula**:
For a source moving away from the observer, the observed frequency \( v' \) can be expressed as:
\[ v' = \frac{v \cdot c}{c + b} \]
This indicates that the observed frequency decreases as the star moves away.

**Hint**: Remember that the frequency and wavelength are related by the equation \( \lambda = \frac{c}{v} \).

4. **Relate Frequency to Wavelength**:
The wavelength \( \lambda' \) observed by the observer can be calculated using the relationship between speed, frequency, and wavelength:
\[ \lambda' = \frac{c}{v'} \]
Substituting the expression for \( v' \) from the previous step, we get:
\[ \lambda' = \frac{c}{\frac{v \cdot c}{c + b}} = \frac{(c + b)}{v} \]

5. **Conclusion on Wavelength**:
Since \( b \) (the speed of the star) is positive, it follows that \( \lambda' > \lambda \). This means that the observed wavelength of light from the star is increased.

**Hint**: Think about how the increase in wavelength corresponds to a decrease in frequency.

### Final Answer:
An observer on Earth will see the wavelength of light coming from the star as increased.