Notes from Toppers
Physics  Power of a Lens and Combination of Thin Lenses in Contact Detailed Notes
Reference: NCERT Physics, Class 11 and Class 12
1. Power of a Lens
 Definition: The power of a lens is defined as the ability to converge (or diverge) light rays.
 Formula: P = 1/f, where P is the power in dioptres (D), and f is the focal length in meters.
 Units: The SI unit of power is dioptres (D). 1 dioptre is the power of a lens with a focal length of 1 meter.
 Sign Conventions:
 Convex lenses (converging) are assigned positive (+) sign.
 Concave lenses (diverging) are assigned a negative () sign.
 Relationship with Focal Length:
 Lenses with shorter focal lengths have higher power.
 Lenses with longer focal lengths have lower power.
2. Combination of Thin Lenses in Contact
 Effective Focal Length (f_e): When two thin lenses are placed in contact, the effective focal length (f_e) is given by: 1/f_e = 1/f_1 + 1/f_2, where f_1 and f_2 are the focal lengths of the individual lenses.
 Effective Power (P_e): The effective power (P_e) of lenses in contact is given by: P_e = P_1 + P_2, where P_1 and P_2 are the powers of the individual lenses.
 Special Cases:
 If two lenses have the same power (P_1 = P_2), f_e = f_1/2 and P_e = 2P_1.
 If one lens has infinite focal length (f_2 = ∞), f_e = f_1 and P_e = P_1.
 If a lens is placed in contact with a plane mirror (f_2 = ∞), f_e = f_1/2 and P_e = 2P_1.
3. Magnification

Definition: Magnification (m) is the ratio of the size of the image (h’) to the size of the object (h).

Lateral Magnification (m_l): It refers to the ratio of the image height to the object height, m_l = h’/h.

Angular Magnification (m_a): It refers to the ratio of the angle subtended by the image (θ’) to the angle subtended by the object (θ), m_a = θ’/θ.

Formula for Lenses:

Convex Lens: m_l = v/u, where v is the image distance and u is the object distance.

Concave Lens: m_l = v/u, where v is the virtual image distance and u is the object distance.

Magnifying Power of Microscope: m = m_l(D/f_0), where m_l is the lateral magnification, D is the distance of distinct vision (25 cm), and f_0 is the focal length of the objective lens.
4. Ray Diagrams and Graphical Analysis
 Ray diagrams are used to graphically trace the path of light rays through lenses and lens combinations.
 Parallel rays from the object are traced through the lens to determine the location of the image.
 Focal points and principal axes of the lenses help in constructing the ray diagrams.
 Ray diagrams are useful in understanding image formation, determining the image type, and calculating the focal length and magnification.
5. Lens Maker’s Formula
 It relates the focal length of a lens to the radii of curvature (R_1 and R_2) of its surfaces: 1/f = (n  1) * (1/R_1  1/R_2), where n is the refractive index of the lens material.
6. Thin Lens Equation and ObjectImage Relationships
 Thin Lens Equation: It describes the relationship between the object distance (u), the image distance (v), and the focal length (f) of a thin lens: 1/f = 1/u + 1/v.
 ObjectImage Relationships:
 For a convex lens, u > 0 (real object), v > 0 (real image), and u < 0 (virtual object), v < 0 (virtual image).
 For a concave lens, u > 0 (real object), v is negative (virtual image), and u < 0 (virtual object), v > 0 (real image).
7. Image Formation and Characteristics
 Real Image: Formed by the convergence of light rays after passing through the lens. Can be projected onto a surface.
 Virtual Image: Formed by the apparent divergence of light rays after passing through the lens. Cannot be projected onto a surface.
 Characteristics:
 Convex Lens: Real and inverted (for real objects), virtual and upright (for virtual objects).
 Concave Lens: Always virtual and upright.
8. Applications
 Optical instruments (telescopes, microscopes, cameras, etc.): Utilize the properties of lenses to magnify images or focus light.
 Eyeglasses and contact lenses: Correct vision problems (nearsightedness, farsightedness, etc.) by adjusting the focal length of the eye’s lens.
 Laser technology: Uses lenses to focus and direct laser beams.