Optics

Step 1: Understanding the Concept:
Total Internal Reflection (TIR) is an optical phenomenon where a wave of light striking the interface between two media is not refracted into the second medium but is entirely reflected back into the first medium. This question asks for the necessary conditions for TIR to occur.
Step 2: Detailed Explanation:
There are two fundamental conditions that must be met for total internal reflection to happen:
1. Direction of Travel: The light must be traveling from a medium with a higher refractive index (optically denser) to a medium with a lower refractive index (optically rarer). Therefore, statement B is correct and statement C is incorrect.
2. Angle of Incidence: The angle of incidence ( ) in the denser medium must be greater than a specific angle called the critical angle ( ). Therefore, statement A is correct.
Additionally, let's analyze statement D:
The critical angle is defined by Snell's Law when the angle of refraction is 90\textdegree. If is the refractive index of the denser medium and is that of the rarer medium, then:


This formula clearly shows that the critical angle depends on the refractive indices of both media. Therefore, statement D is correct.
Step 3: Final Answer:
The true statements are A, B, and D.

Step 1: Understanding the Concept:
This question tests fundamental principles of wave propagation, specifically how frequency behaves in different media and the conservation of energy at an interface.
Step 2: Detailed Explanation:
Statement A and B:
The frequency of a wave is determined by its source. When a wave passes through a linear medium, the medium responds proportionally to the wave's oscillations, so the frequency remains constant. In a non-linear medium, the medium's properties depend on the wave's amplitude. This non-linear response can generate new frequencies, such as harmonics (multiples of the original frequency). Therefore, the frequency can change in a non-linear medium but remains constant in a linear one.
Statement A is correct, and statement B is incorrect.
Statement C and D:
The reflection coefficient (R) is the ratio of reflected wave intensity to incident wave intensity ( ). The transmission coefficient (T) is the ratio of transmitted wave intensity to incident wave intensity ( ).
According to the principle of conservation of energy, the total energy of the incident wave at an interface must equal the sum of the energies of the reflected and transmitted waves, assuming there is no absorption of energy at the interface.

Dividing the entire equation by , we get:

Therefore, statement C is correct, and statement D, which violates the conservation of energy, is incorrect.
Step 3: Final Answer:
The correct statements are A and C.

Step 1: Understanding the Concept:
This question requires matching different types of monochromatic optical aberrations with their resulting effect on the image.
Step 2: Detailed Explanation:
Let's analyze the best description for each aberration from the given list:


A. Spherical aberration: Occurs when light rays passing through different parts of a spherical lens focus at different points. This causes an on-axis point object to be imaged not as a sharp point, but as a blurred surface. So, A matches IV.
B. Coma: An off-axis aberration that makes an off-axis point object appear as a comet-shaped blur. A simplified description of this blur, particularly its head, is an image of a point object as a disc. So, B matches I.
C. Astigmatism: An off-axis aberration where rays in different planes (e.g., vertical and horizontal) focus at different distances from the lens. This causes the focal points to be spread out along the optical axis, with two distinct line foci. This can be described as the spreading of the image along the principal axis. So, C matches II.
D. Distortion: Occurs when the magnification of the lens varies with distance from the optical axis. This does not blur the image but deforms its shape. For example, a straight line in the object that does not pass through the center will be imaged as a curved line. Thus, a Line object is not imaged into a (straight) line. So, D matches III.

Step 3: Final Answer:
Based on the most plausible interpretation of the descriptions, the correct matching is A-IV, B-I, C-II, D-III.