Power of a Lens and Combination of Thin Lenses in Contact - Some examples on refraction through lens

  • Recap: Lens Equation
    • $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
      • $f$ = focal length of the lens
      • $v$ = image distance
      • $u$ = object distance
  • Power of a Lens
    • The power of a lens is defined as the reciprocal of its focal length.
      • Power ($P$) = $\frac{1}{f}$
      • Unit: Dioptre (D)
  • Example 1: Convex Lens
    • Consider a convex lens with a focal length of 10 cm.
    • Find the power of the lens.
      • $P = \frac{1}{f} = \frac{1}{10} = 0.1$ D
  • Example 2: Concave Lens
    • Consider a concave lens with a focal length of -12 cm.
    • Find the power of the lens.
      • $P = \frac{1}{f} = \frac{1}{-12} = -0.083$ D
  • Combination of Thin Lenses in Contact
    • When two thin lenses are placed in contact with each other, the effective focal length ($f$) and power ($P$) can be calculated using the formula:
      • $\frac{1}{f} = \Sigma{\frac{1}{f_i}}$
      • $P = \Sigma{P_i}$
  • Example 3: Combination of Convex and Concave Lens
    • Consider a convex lens with a focal length of 20 cm and a concave lens with a focal length of -15 cm, placed in contact with each other.
    • Find the effective focal length and power of the combination.
      • $\frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} = \frac{1}{20} + \frac{1}{-15} = -0.033$ cm$^{-1}$
      • $P = P_1 + P_2 = \frac{1}{f_1} + \frac{1}{f_2} = \frac{1}{20} + \frac{1}{-15} = -0.033$ D
  • Example 4: Combination of Two Convex Lenses
    • Consider two convex lenses with focal lengths of 30 cm and 15 cm, placed in contact with each other.
    • Find the effective focal length and power of the combination.
      • $\frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} = \frac{1}{30} + \frac{1}{15} = 0.05$ cm$^{-1}$
      • $P = P_1 + P_2 = \frac{1}{f_1} + \frac{1}{f_2} = \frac{1}{30} + \frac{1}{15} = 0.05$ D
  • Example 5: Combination of Two Concave Lenses
    • Consider two concave lenses with focal lengths of -25 cm and -10 cm, placed in contact with each other.
    • Find the effective focal length and power of the combination.
    • $\frac{1}{f} = \frac{1}{f_1} + \frac{1}{f_2} = \frac{1}{-25} + \frac{1}{-10} = -0.06$ cm$^{-1}$
    • $P = P_1 + P_2 = \frac{1}{f_1} + \frac{1}{f_2} = \frac{1}{-25} + \frac{1}{-10} = -0.06$ D

Power of a Lens and Combination of Thin Lenses in Contact

  • Recap: Lens Equation
    • $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
    • $f$ = focal length of the lens
    • $v$ = image distance
    • $u$ = object distance

Power of a Lens and Combination of Thin Lenses in Contact

  • Power of a Lens
    • The power of a lens is defined as the reciprocal of its focal length.
    • Power ($P$) = $\frac{1}{f}$
    • Unit: Dioptre (D)

Power of a Lens and Combination of Thin Lenses in Contact

  • Example 1: Convex Lens
    • Consider a convex lens with a focal length of 10 cm.
    • Find the power of the lens.
    • $P = \frac{1}{f} = \frac{1}{10} = 0.1$ D

Power of a Lens and Combination of Thin Lenses in Contact

  • Example 2: Concave Lens
    • Consider a concave lens with a focal length of -12 cm.
    • Find the power of the lens.
    • $P = \frac{1}{f} = \frac{1}{-12} = -0.083$ D

Power of a Lens and Combination of Thin Lenses in Contact

  • Combination of Thin Lenses in Contact
    • When two thin lenses are placed in contact with each other, the effective focal length and power can be calculated.
    • $\frac{1}{f} = \Sigma{\frac{1}{f_i}}$
    • $P = \Sigma{P_i}$

Power of a Lens and Combination of Thin Lenses in Contact

  • Example 3: Combination of Convex and Concave Lens
    • Consider a convex lens with a focal length of 20 cm and a concave lens with a focal length of -15 cm, placed in contact with each other.
    • Find the effective focal length and power of the combination.
    • $\frac{1}{f} = \frac{1}{20} + \frac{1}{-15} = -0.033$ cm$^{-1}$
    • $P = \frac{1}{f} = -0.033$ D

Power of a Lens and Combination of Thin Lenses in Contact

  • Example 4: Combination of Two Convex Lenses
    • Consider two convex lenses with focal lengths of 30 cm and 15 cm, placed in contact with each other.
    • Find the effective focal length and power of the combination.
    • $\frac{1}{f} = \frac{1}{30} + \frac{1}{15} = 0.05$ cm$^{-1}$
    • $P = \frac{1}{f} = 0.05$ D

Power of a Lens and Combination of Thin Lenses in Contact

  • Example 5: Combination of Two Concave Lenses
    • Consider two concave lenses with focal lengths of -25 cm and -10 cm, placed in contact with each other.
    • Find the effective focal length and power of the combination.
    • $\frac{1}{f} = \frac{1}{-25} + \frac{1}{-10} = -0.06$ cm$^{-1}$
    • $P = \frac{1}{f} = -0.06$ D

Power of a Lens and Combination of Thin Lenses in Contact

  • Recap: Lens Equation
    • $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
    • $f$ = focal length of the lens
    • $v$ = image distance
    • $u$ = object distance

Power of a Lens and Combination of Thin Lenses in Contact

  • Power of a Lens
    • The power of a lens is defined as the reciprocal of its focal length.
    • Power ($P$) = $\frac{1}{f}$
    • Unit: Dioptre (D) ``

Power of a Lens and Combination of Thin Lenses in Contact

  • Recap: Lens Equation
    • $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
    • $f$ = focal length of the lens
    • $v$ = image distance
    • $u$ = object distance

Power of a Lens and Combination of Thin Lenses in Contact

  • Power of a Lens
    • The power of a lens is defined as the reciprocal of its focal length.
    • Power ($P$) = $\frac{1}{f}$
    • Unit: Dioptre (D)

Power of a Lens and Combination of Thin Lenses in Contact

  • Example 1: Convex Lens
    • Consider a convex lens with a focal length of 10 cm.
    • Find the power of the lens.
    • $P = \frac{1}{f} = \frac{1}{10} = 0.1$ D

Power of a Lens and Combination of Thin Lenses in Contact

  • Example 2: Concave Lens
    • Consider a concave lens with a focal length of -12 cm.
    • Find the power of the lens.
    • $P = \frac{1}{f} = \frac{1}{-12} = -0.083$ D

Power of a Lens and Combination of Thin Lenses in Contact

  • Combination of Thin Lenses in Contact
    • When two thin lenses are placed in contact with each other, the effective focal length and power can be calculated.
    • $\frac{1}{f} = \Sigma{\frac{1}{f_i}}$
    • $P = \Sigma{P_i}$

Power of a Lens and Combination of Thin Lenses in Contact

  • Example 3: Combination of Convex and Concave Lens
    • Consider a convex lens with a focal length of 20 cm and a concave lens with a focal length of -15 cm, placed in contact with each other.
    • Find the effective focal length and power of the combination.
    • $\frac{1}{f} = \frac{1}{20} + \frac{1}{-15} = -0.033$ cm$^{-1}$
    • $P = \frac{1}{f} = -0.033$ D

Power of a Lens and Combination of Thin Lenses in Contact

  • Example 4: Combination of Two Convex Lenses
    • Consider two convex lenses with focal lengths of 30 cm and 15 cm, placed in contact with each other.
    • Find the effective focal length and power of the combination.
    • $\frac{1}{f} = \frac{1}{30} + \frac{1}{15} = 0.05$ cm$^{-1}$
    • $P = \frac{1}{f} = 0.05$ D

Power of a Lens and Combination of Thin Lenses in Contact

  • Example 5: Combination of Two Concave Lenses
    • Consider two concave lenses with focal lengths of -25 cm and -10 cm, placed in contact with each other.
    • Find the effective focal length and power of the combination.
    • $\frac{1}{f} = \frac{1}{-25} + \frac{1}{-10} = -0.06$ cm$^{-1}$
    • $P = \frac{1}{f} = -0.06$ D

Power of a Lens and Combination of Thin Lenses in Contact

  • Recap: Lens Equation
    • $\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$
    • $f$ = focal length of the lens
    • $v$ = image distance
    • $u$ = object distance

Power of a Lens and Combination of Thin Lenses in Contact

  • Power of a Lens
    • The power of a lens is defined as the reciprocal of its focal length.
    • Power ($P$) = $\frac{1}{f}$
    • Unit: Dioptre (D) ``