(a) Clearly, the ray in medium B is moving towards normal when it enters from medium A. Hence, medium B is optically denser than medium A. This means that the refractive index of medium B with respect to refractive index of medium A will be greater than 1.
(b) The refractive index (n) of medium B with respect to medium A can be calculated using the formula:
n = Va / Vb
where, Va is the speed of light in medium A and Vb is the speed of light in medium B.
So, if the speed of light in medium A is Va and in medium B is Vb, the refractive index of medium B with respect to medium A can be calculated as:
n = Va / Vb
Refractive index is a fundamental property of optical media that determines how light propagates through them. It is defined as the ratio of the speed of light in a vacuum (c) to the speed of light in the medium (v).
When light travels from one medium to another, it changes direction, a process known as refraction. The amount of refraction that occurs depends on the refractive index of the two media and the angle at which the light enters the new medium.
The refractive index of a medium is a measure of how much the medium slows down the speed of light. A higher refractive index indicates that light will travel more slowly through the medium, while a lower refractive index indicates that light will travel more quickly through the medium.
The refractive index is an important parameter in many optical applications, such as lenses, prisms, and optical fibers. It is also used in spectroscopy to identify the chemical composition of a substance by measuring the refractive index of light passing through it.