Step 1: Explain Rayleigh Scattering. When sunlight enters the Earth's atmosphere, it interacts with the tiny gas molecules (mostly nitrogen and oxygen). This interaction causes the light to be scattered in all directions. Rayleigh scattering is most effective for shorter wavelengths of light. The intensity of scattering is inversely proportional to the fourth power of the wavelength (\(I \propto 1/\lambda^4\)).
Step 2: Apply scattering to the blue sky. Blue and violet light have the shortest wavelengths in the visible spectrum, so they are scattered much more strongly than longer wavelengths like red and yellow. When we look at the sky away from the sun, we see this scattered blue light coming from all directions, which is why the sky appears blue.
Step 3: Apply scattering to sunrise and sunset. At sunrise or sunset, sunlight has to travel through a much thicker layer of the atmosphere to reach our eyes. By the time the light reaches us, most of the blue and green light has been scattered away from our line of sight. The remaining light that passes through directly is rich in longer wavelengths, such as red, orange, and yellow, making the sun and the sky around it appear reddish.
Light from a point source in air falls on a spherical glass surface (refractive index, \( \mu = 1.5 \) and radius of curvature \( R = 50 \) cm). The image is formed at a distance of 200 cm from the glass surface inside the glass. The magnitude of distance of the light source from the glass surface is 1cm.