Optics

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 ( ) 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 IV - B II - C III - D I This corresponds to option (1).

Step 1: Recall the formula for the resolving power of a diffraction grating. The resolving power is defined as , where is the smallest wavelength difference that can be distinguished at wavelength . The formula for a grating is: where is the spectral order (an integer) and is the total number of lines (or rulings) on the grating.
Step 2: Analyze the given statements based on the formula. - A. increases with increase in total number of lines (N): From , it is clear that if increases, increases. This statement is correct. - B. increases with increase in total width of grating (W): The total width is related to and the grating element by . The grating equation is . Substituting gives . So, . Thus, resolving power is directly proportional to the total width . This statement is correct. - C. increases with increasing the order of spectrum (m): From , if increases, increases. An Echelon grating is specifically designed to work at very high orders ( ), giving it very high resolving power. This statement is correct. - D. increases with decreasing the order of spectrum: This is the opposite of C and is incorrect.
Step 3: Conclude the correct statements. Statements A, B, and C are correct descriptions of the factors affecting the resolving power of a grating.

Step 1: Recall the formula for specific rotation. Specific rotation is defined as: where is the observed optical rotation in degrees, is the path length in decimeters (dm), and is the concentration of the solution in g/cc (or g/mL).
Step 2: Convert the given units to the required units. - Observed rotation: . - Path length: (since 1 dm = 10 cm). - Concentration: Mass = 20 g, Volume = 50 cc.
Step 3: Calculate the specific rotation.
Step 4: Match the result with the options. The calculated value is approximately 66.9 degree (decimeter) (g/cc) .

Step 1: Analyze each condition for sustained interference. - A. Coherence: The sources must be coherent, meaning they must maintain a constant phase relationship. This is the most fundamental condition for interference to be observable. If the phase relationship changes randomly, the interference pattern will wash out. So, A is true. - B. Propagation along the same line: For interference to occur, the waves must overlap in space. While they don't have to be perfectly collinear, they must be propagating in nearly the same direction to produce a stable interference pattern. So, B is considered a necessary condition. - C. Equal amplitude: For maximum contrast between bright and dark fringes (i.e., perfect destructive interference where intensity is zero), the amplitudes of the interfering waves should be equal. While interference can be observed with unequal amplitudes, the condition for ideal, sustained interference often includes equal amplitudes for best visibility. So, C is a condition for ideal interference. - D. Same state of polarization: Two light waves with perpendicular polarization cannot interfere. For interference to occur, the electric field vectors of the waves must have components along the same direction. Therefore, they must be in the same state of polarization. So, D is true.
Step 2: Conclude the set of true conditions. All four statements (A, B, C, and D) represent the ideal conditions required to observe a clear, stable, and high-contrast interference pattern.

This question requires knowledge of the approximate refractive indices of common materials. We can match them by considering their typical values. - D. Diamond: Diamond is famous for its very high refractive index, which gives it its brilliance. The highest value in the list is 2.417. So, D matches IV. - A. Ice: Ice is frozen water, and its refractive index is close to that of water (which is about 1.33). The lowest value in the list is 1.309, which is a very reasonable value for ice. So, A matches I. - B. Rock salt (NaCl): This is a crystalline solid. Its refractive index is known to be in the mid-range, typically around 1.54. So, B matches III. - C. CCl4 (Carbon Tetrachloride): This is a dense organic liquid. Its refractive index is typically in the mid-range, lower than that of rock salt. The value 1.460 is correct for CCl4. So, C matches II. The correct set of matches is A - I, B - III, C - II, D - IV.