Which of the following statements are correct?
(A) Total internal reflection occurs when a ray of light travels from a rarer transparent medium to a denser medium.
(B) In total internal reflection, the incident ray of light remains in the same mediumafter reflection.
(C) In total internal reflection, the angle of incidence inside the denser transparent medium is equal to the angle of reflection in the same medium.
(D) In total internal reflection inside a denser medium there is no angle of refraction

Choose the correct answer from the options given below:

The correct answer is (B), (C) and (D) only.

Let's analyze each statement step-by-step to understand why they are correct or incorrect:

Statement (A): "Total internal reflection occurs when a ray of light travels from a rarer transparent medium to a denser medium."
This statement is incorrect. For total internal reflection to occur, light must travel from an optically denser medium (having a higher refractive index) to an optically rarer medium (having a lower refractive index). When light travels in this direction, it bends away from the normal, which allows the angle of refraction to reach $90°$ at the critical angle, and subsequently undergo reflection at larger angles.

Statement (B): "In total internal reflection, the incident ray of light remains in the same medium after reflection."
This statement is correct. In total internal reflection, when the angle of incidence exceeds the critical angle, the boundary between the two media acts as a perfect mirror. As a result, the entire incident light is reflected back into the denser medium, meaning the ray remains within the same medium.

Statement (C): "In total internal reflection, the angle of incidence inside the denser transparent medium is equal to the angle of reflection in the same medium."
This statement is correct. Since total internal reflection is a form of reflection, it strictly obeys the laws of reflection. Therefore, the angle of incidence, denoted as:
$${\theta }_i$$
is always equal to the angle of reflection, denoted as:
$${\theta }_r$$
giving the relation:
$${\theta }_i={\theta }_r$$

Statement (D): "In total internal reflection inside a denser medium there is no angle of refraction"
This statement is correct. Because all of the light is reflected back into the first medium, there is no transmitted (refracted) ray entering the second medium. Since there is no refracted ray, an angle of refraction does not exist.

Therefore, statements (B), (C), and (D) are correct, which matches the option (B), (C) and (D) only.