Step 1: Analyze each phenomenon in List-I and match it with the underlying principle in List-II.
- A. Compton Effect: This involves the change in wavelength of an X-ray photon when it collides with an electron. It is a classic example of particle-like Scattering. This matches IV.
- B. Colors in thin film: The vibrant colors seen in soap bubbles or oil slicks are caused by the constructive and destructive Interference of light waves reflecting off the top and bottom surfaces of the thin film. This matches II.
- C. Double Refraction: Certain crystals, like calcite, split an unpolarized light beam into two separate, plane-polarized beams. This phenomenon is a direct consequence of the Polarization of light. This matches III.
- D. Bragg's Equation: This equation (\(n\lambda = 2d\sin\theta\)) describes the condition for constructive interference of waves scattered by crystal planes. It is the fundamental principle of X-ray Diffraction. This matches I.
Step 2: Assemble the correct pairings.
- A \(\rightarrow\) IV
- B \(\rightarrow\) II
- C \(\rightarrow\) III
- D \(\rightarrow\) I
This corresponds to option (1).