Review the key concepts, formulae, and examples before starting your quiz.
🔑Concepts
Dispersion of Light: The phenomenon of splitting of a beam of white light into its constituent seven colors (VIBGYOR) when passed through a transparent medium like a glass prism. This happens because different colors of light travel at different speeds in glass, though they travel at the same speed in vacuum.
Cause of Dispersion: The refractive index of a medium depends on the wavelength of light. According to Cauchy's relation, . Since , the refractive index for red light is less than that for violet light (), causing red to deviate the least and violet to deviate the most.
Electromagnetic Spectrum: The complete range of electromagnetic waves arranged in order of increasing frequency or decreasing wavelength. The sequence is: Radio waves, Microwaves, Infrared (IR), Visible light, Ultraviolet (UV), X-rays, and Gamma rays (-rays).
Visible Spectrum: The narrow band of the EM spectrum visible to the human eye, ranging from approximately () for violet to () for red light.
Infrared Radiation: These are heat radiations with wavelengths longer than red light (). They are detected using a thermopile or a blackened bulb thermometer. They do not affect ordinary photographic film but affect special infrared films.
Ultraviolet Radiation: These have wavelengths shorter than violet light (). They can be detected by their chemical effect on silver chloride () solution, which turns violet and then black. UV rays are absorbed by the Ozone layer in the atmosphere.
Scattering of Light: The process where light is absorbed by atmospheric particles and re-emitted in all directions. According to Rayleigh's law of scattering, the intensity of scattered light is inversely proportional to the fourth power of the wavelength: . This explains why the sky appears blue (shorter wavelengths scatter more) and the sun appears red at sunrise/sunset (longer wavelengths reach the observer).
📐Formulae
💡Examples
Problem 1:
A beam of monochromatic light has a wavelength of in air. It enters a glass slab of refractive index . Calculate the wavelength of light in glass.
Solution:
Given: , . We use the formula . Therefore, .
Explanation:
When light enters a denser medium, its speed decreases but its frequency remains constant. This results in a proportional decrease in wavelength.
Problem 2:
Compare the scattering of blue light () and red light () in the atmosphere.
Solution:
According to Rayleigh's Law, . The ratio of scattering is . Substituting the values: .
Explanation:
Blue light is scattered times more than red light because it has a shorter wavelength, which is why the sky appears blue.