Optics

Real, inverted, and same size as the object

Step 1: For a convex lens, the centre of curvature C is the same as 2F (twice the focal length from the optical centre). Step 2: When an object is placed at 2F (centre of curvature), the image is formed at 2F on the other side of the lens. Step 3: This means the image distance equals the object distance, so the image is the same size as the object (magnification = 1). Step 4: Since the image is formed on the other side of the lens, it is a real image. Step 5: All real images formed by a convex lens are inverted. Therefore, the image is real, inverted, and of the same size.

1/f = 1/v - 1/u

Step 1: The lens formula is a standard formula used to find the position of images formed by lenses. Step 2: The correct formula is 1/f = 1/v − 1/u, where u is the object distance, v is the image distance, and f is the focal length. Step 3: The sign convention is important — distances are measured from the optical centre; distances in the direction of incident light are positive and opposite are negative. Step 4: The option 1/f = 1/u + 1/v is wrong — it ignores the sign convention between image and object distances. Step 5: This formula applies to both convex and concave lenses when proper sig

-2 D

Step 1: Power of a lens P = 1/f, where f must be in metres. Step 2: A concave lens has a negative focal length by convention, so f = -0.5 m. Step 3: P = 1/f = 1/(-0.5) = -2 D. Step 4: The negative sign confirms it is a concave (diverging) lens — concave lens always has negative power. Step 5: The option +2 D would be the power of a convex lens with f = +0.5 m, which is incorrect for a concave lens. The unit of power is dioptre (D).

Tyndall scattering

Step 1: There are four main types of scattering — Rayleigh, Mie, Tyndall, and Raman. Step 2: Rayleigh scattering is caused by gas molecules in the atmosphere (explains blue sky). Step 3: Mie scattering occurs when the scatterer is similar in size to the wavelength of light (explains white clouds). Step 4: Tyndall scattering specifically refers to the scattering of light by colloidal particles in a colloidal solution — for example, when a beam of light passes through milk or muddy water, its path becomes visible. Step 5: Raman scattering involves a change in the frequency/wavelength of scattere