The correct answer is option 1, which states that statements 1 and 4 are correct. Let`s break down each statement to understand why.

Statement 1: The formation of a mirage in the desert can be explained by the principle of total internal reflection. When light passes from a denser medium (such as air) to a rarer medium (such as hot sand), it can undergo total internal reflection at the boundary due to the abrupt change in refractive index. This can create an optical illusion, making distant objects appear as if they are reflected in a body of water.

Statement 2: The formation of an image in a microscope is not solely explained by the principle of total internal reflection. While total internal reflection does play a role in some aspects of microscope imaging, other factors such as lens systems and light scattering also contribute to the formation of an image.

Statement 3: The color of the evening sky is not directly explained by the principle of total internal reflection. The color of the sky is mainly due to scattering of sunlight by the Earth`s atmosphere, particularly by tiny particles and molecules that cause the scattering of shorter wavelengths (blue and violet light) more than longer wavelengths (red and orange light).

Statement 4: The operation of optical fibers does rely