Ray Optics And Optical Instruments

The blue color of the sky is primarily due to a phenomenon called Rayleigh scattering. Rayleigh scattering occurs when light interacts with particles or molecules that are smaller than the wavelength of the light. In the Earth's atmosphere, the molecules of nitrogen and oxygen are responsible for this scattering.

When sunlight enters the Earth's atmosphere, it contains a wide range of colors, including all the colors of the visible spectrum. However, blue light has a shorter wavelength and is scattered more efficiently by the molecules in the atmosphere compared to other colors.

As the sunlight passes through the atmosphere, the blue light is scattered in all directions by the nitrogen and oxygen molecules. This scattered blue light eventually reaches our eyes from all directions, giving the sky its blue appearance.

It is important to note that the scattering of blue light is more prominent in the Earth's atmosphere during the daytime. During sunrise and sunset, the light passes through a larger portion of the atmosphere, resulting in longer path lengths and greater scattering. This leads to the beautiful hues of red, orange, and pink observed during those times.

In summary, the blue color of the sky is primarily due to the scattering of shorter-wavelength blue light by the molecules in the Earth's atmosphere, a phenomenon known as Rayleigh scattering.

The lens maker's formula relates the focal length of a lens to the refractive index of the lens relative to the surrounding medium, and the radii of curvature and of the lens surfaces: The power of a lens is the reciprocal of its focal length: Let be the refractive index of the lens, and let be the refractive index of water. In air, the power of the lens is so which simplifies to In water, the power of the lens is Final Answer: 1.25.

Step 1: Apply the formula for wave speed in a string. where is the tension and is the linear mass density ( ).
Step 2: Calculate the ratio of wave speeds. For string 1 ( ) and string 2 ( ):

The resultant intensity at a point in an interference pattern is given by where and are the intensities of the two sources, and is the phase difference between them. At point A, the phase difference is , so At point B, the phase difference is , so The difference in intensities is .
Final Answer: .