The correct answer is option 4, "Red shift."

Option 1: Twinkling of stars can be attributed to the refraction of light. When light from stars passes through the Earth`s atmosphere, it undergoes refraction due to the varying density of air. This refraction causes the apparent brightness of stars to fluctuate, giving them a twinkling appearance.

Option 2: Mirage is also a phenomenon that can be explained by the refraction of light. It occurs when light rays passing through different regions of air with different temperatures and densities are bent, creating an optical illusion of water or objects that are not actually present.

Option 3: The formation of a rainbow is a result of both reflection and refraction of light. When sunlight passes through raindrops, it undergoes refraction and dispersion, causing the different colors of light to separate and form a circular arc.

Option 4: Red shift is the phenomenon where light from distant galaxies appears to be shifted towards longer wavelengths, indicating that the objects are moving away from us. This is not a result of refraction, but rather the Doppler effect, which occurs due to relative motion between the source of light and the observer.

Therefore, option 4, "Red shift" cannot be attributed