(A): Violet shift indicates that a star is approaching the earth.
(R): Violet shift indicates decrease in apparent wavelength of light.

Options

A. Both 'A' and 'R' are true and 'R' is the correct, explanation of 'A'.
B. Both 'A' and 'R' are true and 'R' is not the correct explanation of 'A'
C. A' is true and 'R' is false
D. Both 'A' and 'R' are false

Answer

To solve the question regarding the statements about violet shift, we need to analyze both statements (A) and (R) separately.

### Step 1: Understand Statement (A)
Statement (A) claims that "Violet shift indicates that a star is approaching the earth."

- The term "violet shift" refers to the phenomenon where the light from an object is shifted towards the violet end of the spectrum. This occurs when the object is moving towards the observer (in this case, the Earth).
- Therefore, this statement is **True**.

### Step 2: Understand Statement (R)
Statement (R) claims that "Violet shift indicates a decrease in apparent wavelength of light."

- When an object moves towards an observer, the wavelengths of light emitted by the object are compressed, leading to a decrease in the wavelength. This is known as a blue shift, but in the context of the visible spectrum, the term "violet shift" can be used to describe the same effect when the shift is significant enough to move light towards the violet end.
- Thus, this statement is also **True**.

### Step 3: Analyze the Relationship Between (A) and (R)
Now we need to determine if (A) is a correct explanation of (R).

- Since both statements are true, and (A) provides a correct explanation of (R), we can conclude that the relationship is valid.

### Final Conclusion
Both statements (A) and (R) are true, and (A) is the correct explanation of (R).

### Summary of the Solution:
1. Statement (A) is true: Violet shift indicates that a star is approaching the Earth.
2. Statement (R) is true: Violet shift indicates a decrease in apparent wavelength of light.
3. (A) is a correct explanation of (R).