The twinkling of stars is due to the atmospheric refraction of light. As light from a star passes through the Earth's atmosphere, it encounters layers of air with varying temperatures and densities. These layers act like prisms, bending (refracting) the light. Since the atmosphere is constantly changing, the amount of bending varies continuously. This causes the star's apparent position and brightness to fluctuate, making it appear to twinkle.
Reflection is the bouncing back of light from a surface.
Total internal reflection occurs when light travels from a denser medium to a rarer medium at an angle of incidence greater than the critical angle. Dispersion is the splitting of white light into its constituent colors.
If \( r \) and \( r' \) denote the angles inside the prism having angle of prism \( 50^\circ \), considering that during the interval of time from \( t = 0 \) to \( t = T \), \( r \) varies with time as \( r = 10^\circ + t^2 \). During this time \( r' \) will vary with time as