Optics

When the Sun is near the horizon during the morning or evening, it appears reddish. The phenomenon that is responsible for this observation is

[amp_mcq option1=”reflection of light” option2=”refraction of light” option3=”dispersion of light” option4=”scattering of light” correct=”option4″]

The phenomenon responsible for the reddish appearance of the Sun near the horizon is scattering of light, specifically Rayleigh scattering. As sunlight passes through a longer path in the Earth’s atmosphere during sunrise or sunset, shorter wavelengths (blue and violet) are scattered away more effectively by air molecules than longer wavelengths (red and orange). The light that reaches the observer’s eyes is therefore enriched in the longer, redder wavelengths.

– Rayleigh scattering is inversely proportional to the fourth power of the wavelength (scattering ∝ 1/λ⁴), meaning shorter wavelengths are scattered much more than longer wavelengths.
– The path length of sunlight through the atmosphere is longest at sunrise and sunset.

Reflection is the bouncing of light off a surface. Refraction is the bending of light as it passes from one medium to another (e.g., causing the sun’s image to appear flattened at the horizon). Dispersion is the splitting of white light into its constituent colors based on wavelength (as in a prism or rainbow). While these phenomena occur, scattering is the primary reason for the reddish appearance of the sun and sky color variations.

The optical phenomenon that is primarily responsible for the observation of rainbow on a rainy day is

[amp_mcq option1=”diffraction” option2=”interference” option3=”dispersion” option4=”reflection” correct=”option3″]

A rainbow is formed when sunlight interacts with water droplets suspended in the atmosphere. This phenomenon involves several processes: refraction, dispersion, and reflection.

– When white sunlight enters a water droplet, it is refracted (bent) because the speed of light changes as it passes from air to water.
– As sunlight is composed of different colors (wavelengths), and the refractive index of water is slightly different for each color, the white light is split into its constituent colors. This splitting of white light into its spectrum is called dispersion. Dispersion is crucial because it separates the colors we see in a rainbow.
– The dispersed light then reflects off the inner back surface of the water droplet.
– Finally, the light is refracted again as it exits the droplet into the air, further enhancing the separation of colors.

While refraction and reflection are necessary parts of the process, dispersion is the specific phenomenon responsible for separating the different wavelengths of light (colors) that make up the visible spectrum, thereby creating the band of colors characteristic of a rainbow. Diffraction and interference are wave phenomena but are not the primary cause of the color separation in a typical rainbow.

A photon of X-ray has energy of 1 keV. A photon of visible radiation has energy of 3 eV. In this context, which one of the following statements is not correct?

[amp_mcq option1=”The wavelength of X-ray photon is less than the wavelength of visible radiation photon.” option2=”Both the photons have different energies.” option3=”The speeds of both the photons in vacuum are different.” option4=”The frequency of X-ray photon is higher than the frequency of visible radiation photon.” correct=”option3″]

The energy (E), frequency (f), and wavelength (λ) of a photon are related by the equations E = hf and E = hc/λ, where h is Planck’s constant and c is the speed of light in vacuum. The speed of light in vacuum (c) is a universal constant, approximately 3 x 10⁸ m/s, and is the same for all electromagnetic radiations regardless of their energy, frequency, or wavelength.

– The energy of the X-ray photon (1 keV = 1000 eV) is significantly higher than the energy of the visible radiation photon (3 eV).
– Statement A: Since E = hc/λ, higher energy means shorter wavelength. E(X-ray) > E(Visible), so λ(X-ray) < λ(Visible). This statement is correct. - Statement B: The energies (1000 eV and 3 eV) are clearly different. This statement is correct. - Statement C: The speed of all electromagnetic radiation (including photons of X-rays and visible light) in vacuum is the constant 'c'. Their speeds in vacuum are the same, not different. This statement is incorrect. - Statement D: Since E = hf, higher energy means higher frequency. E(X-ray) > E(Visible), so f(X-ray) > f(Visible). This statement is correct.

Electromagnetic radiation spans a wide spectrum of frequencies and wavelengths, each with corresponding energy levels. While energy, frequency, and wavelength vary, the speed of propagation in a vacuum remains constant for all parts of the spectrum.

Consider the electromagnetic radiations having wavelengths 200 nm, 500 nm and 1000 nm. Which wavelength(s) of the following can make visual sensation to a human eye?

[amp_mcq option1=”200 nm and 500 nm” option2=”500 nm and 1000 nm” option3=”500 nm only” option4=”200 nm and 1000 nm” correct=”option3″]

The human eye can make a visual sensation when exposed to electromagnetic radiation within a specific range of wavelengths, known as the visible spectrum. This range is typically considered to be from about 400 nanometers (nm) to 700 nm.

– Wavelengths outside the visible spectrum (like 200 nm which is ultraviolet, and 1000 nm which is infrared) do not cause a visual sensation in humans.
– Out of the given wavelengths, only 500 nm falls within the visible spectrum (approximately 400-700 nm), corresponding to green light.

The visible spectrum is a small part of the entire electromagnetic spectrum. Different wavelengths within the visible spectrum are perceived as different colors by the human eye, ranging from violet (around 400 nm) to red (around 700 nm).

A myopic person has a power of -1.25 Dioptre. What is the focal length and nature of his lens ?

[amp_mcq option1=”50 cm and convex lens” option2=”80 cm and convex lens” option3=”50 cm and concave lens” option4=”80 cm and concave lens” correct=”option4″]

The focal length is 80 cm and the nature of the lens is concave.

– The power of a lens (P) is related to its focal length (f) by the formula P = 1/f, where f is in meters and P is in Dioptres.
– Given P = -1.25 D.
– Focal length f = 1 / P = 1 / (-1.25) meters = -0.8 meters.
– Converting to centimeters: -0.8 meters * 100 cm/meter = -80 cm.
– A negative focal length indicates a concave lens. Myopia (nearsightedness) is corrected using concave lenses to diverge light rays before they reach the eye’s lens.

A convex lens has a positive focal length and is used to correct hyperopia (farsightedness).