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 Object-Image 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.
• Object-Image 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.