Refraction Through a Lens Short notes and Selected PYQs

Lens: A transparent medium bounded by two refracting surfaces, at least one being curved.
Convex Lens (Converging Lens): Thicker at the centre than at the edges. Converges light rays.
Concave Lens (Diverging Lens): Thinner at the centre than at the edges. Diverges light rays.
Principal Axis: The line passing through the centres of curvature of both surfaces.
Optical Centre (O): The central point of a lens through which light passes without deviation.

Principal Focus (F): Point where parallel rays converge (convex) or appear to diverge from (concave) after refraction.
Focal Length (f): Distance between optical centre and principal focus.
Centre of Curvature (C): Centre of the sphere of which the lens surface is a part. Distance from O is radius of curvature (R).
Aperture: Effective diameter of the lens through which refraction occurs.
Relation: R = 2f for thin lenses.

Lens Formula: 1/f = 1/v - 1/u, where f = focal length, v = image distance, u = object distance.
Sign Convention: Distances measured from optical centre. Along principal axis: positive to right, negative to left. Height: positive upward, negative downward.
Magnification (m): m = v/u = Height of Image / Height of Object.
For Convex Lens: f is positive; for concave lens, f is negative.
Power of Lens (P): P = 1/f (in meters). Unit: Dioptre (D). 1 D = 1 m⁻¹.

Object at Infinity: Image at F, real, inverted, highly diminished (point-sized).
Object beyond 2F: Image between F and 2F, real, inverted, diminished.
Object at 2F: Image at 2F on other side, real, inverted, same size.
Object between F and 2F: Image beyond 2F, real, inverted, magnified.
Object at F: Image at infinity, real, inverted, highly magnified.
Object between F and O: Image on same side, virtual, erect, magnified.

For All Object Positions: Image is always virtual, erect, and diminished.
Image Location: Always formed between F and O on same side as object.
Uses: Correction of myopia (short-sightedness), used in combination with convex lens in optical instruments.
Diverging Property: Concave lens always diverges incident light rays.

Convex Lens Uses: Camera, microscope, telescope, magnifying glass, correction of hypermetropia (long-sightedness), projector.
Concave Lens Uses: Correction of myopia, spectacles for near-sighted people, peep holes in doors.
Human Eye: Eye lens is convex; can change focal length (accommodation) to focus on near and far objects.
Defects: Myopia (image forms before retina) corrected by concave lens; Hypermetropia (image forms behind retina) corrected by convex lens.

Refraction Through a Lens