Which of the following are true ?
(1) Speed of light in vacuum is dependent on the direction of propagation.
(2) Speed of light in a madium is independent of the wavelength of light.
(3) The speed of light is independent of the motion of the source. (4) The speed of light in a medium is independent of intensity.
Choose the correct answer from the options given below :

Options

A. `B` and `D` only
B. `C` and `D` only
C. `A` and `C` only
D. `B` and `C` only

Answer

To solve the question, we need to evaluate each statement regarding the speed of light and determine which ones are true.

**Step 1: Analyze Statement 1**
- Statement 1: "Speed of light in vacuum is dependent on the direction of propagation."
- The speed of light in a vacuum is a constant (approximately \(3 \times 10^8\) m/s) and does not depend on the direction of propagation.
- **Conclusion**: This statement is **false**.

**Step 2: Analyze Statement 2**
- Statement 2: "Speed of light in a medium is independent of the wavelength of light."
- The speed of light in a medium is affected by the medium's refractive index, which can vary with the wavelength of light (this phenomenon is known as dispersion).
- **Conclusion**: This statement is **false**.

**Step 3: Analyze Statement 3**
- Statement 3: "The speed of light is independent of the motion of the source."
- According to the theory of relativity, the speed of light in a vacuum is constant and does not change regardless of the motion of the source or observer.
- **Conclusion**: This statement is **true**.

**Step 4: Analyze Statement 4**
- Statement 4: "The speed of light in a medium is independent of intensity."
- The speed of light in a medium is determined by the medium's properties (like refractive index) and is not affected by the intensity of the light.
- **Conclusion**: This statement is **true**.

**Final Conclusion:**
- The true statements are:
- Statement 3: "The speed of light is independent of the motion of the source."
- Statement 4: "The speed of light in a medium is independent of intensity."

Thus, the correct answers are statements 3 and 4.

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