Slide 1:

Power of a Lens and Combination of Thin Lenses in Contact

• The power of a lens is the measure of its ability to converge or diverge light rays.
• It is defined as the reciprocal of the focal length and is denoted by the symbol “P”.
• The unit of power is dioptre (D), and it is represented as 1/metre (m^(-1)).
• The formula for calculating the power of a lens is P = 1/f, where f is the focal length of the lens.
• Positive power indicates a converging lens, while negative power indicates a diverging lens.

Slide 2:

Combination of Thin Lenses in Contact

• When two thin lenses are in contact with each other, they form a combination.
• The power of the combination depends on the powers of the individual lenses and their orientation.
• The formula for calculating the power of a combination of two lenses in contact is given by P_combine = P_1 + P_2, where P_1 and P_2 represent the powers of the individual lenses.
• If both lenses have the same power, the power of the combination doubles.
• The focal length of the combination can be calculated using the formula 1/f_combine = 1/f_1 + 1/f_2, where f_1 and f_2 are the focal lengths of the individual lenses.

Slide 3:

Example 1: Combination of Two Converging Lenses

• Suppose we have a combination of two converging lenses with powers +2 D and +3 D.
• The power of the combination is P_combine = P_1 + P_2 = +2 D + +3 D = +5 D.
• The focal length of the combination can be calculated using the formula 1/f_combine = 1/f_1 + 1/f_2.
• Let’s assume the focal lengths of the individual lenses are f_1 = 0.5 m and f_2 = 0.3 m.
• Plugging these values into the formula, we get 1/f_combine = 1/0.5 + 1/0.3 = 2 + 3.33 = 5.33.
• Therefore, the focal length of the combination is f_combine = 1/5.33 ≈ 0.19 m.

Slide 4:

Example 2: Combination of a Converging Lens and a Diverging Lens

• Consider a combination of a converging lens with power +4 D and a diverging lens with power -2 D.
• The power of the combination is P_combine = P_1 + P_2 = +4 D + (-2 D) = +2 D.
• The focal length of the combination can be calculated using the formula 1/f_combine = 1/f_1 + 1/f_2.
• Assume the focal length of the converging lens is f_1 = 0.25 m and the focal length of the diverging lens is f_2 = -0.5 m.
• Substituting these values into the formula, we get 1/f_combine = 1/0.25 + 1/(-0.5) = 4 + (-2) = 2.
• Therefore, the focal length of the combination is f_combine = 1/2 = 0.5 m.

Slide 5:

Example 3: Combination of Two Diverging Lenses

• Let’s consider a combination of two diverging lenses with powers -3 D and -2 D.
• The power of the combination is P_combine = P_1 + P_2 = -3 D + -2 D = -5 D.
• The focal length of the combination can be calculated using the formula 1/f_combine = 1/f_1 + 1/f_2.
• Assume the focal length of the first lens is f_1 = -0.4 m and the focal length of the second lens is f_2 = -0.5 m.
• Plugging these values into the formula, we get 1/f_combine = 1/(-0.4) + 1/(-0.5) = -2.5 + -2 = -4.5.
• Therefore, the focal length of the combination is f_combine = 1/(-4.5) ≈ -0.22 m.

Slide 6:

Combination of Thin Lenses in Contact - Recap

• When two thin lenses are in contact, they form a combination with a combined power.
• The power of the combination is the sum of the powers of the individual lenses.
• If both lenses have the same power, the power of the combination doubles.
• The focal length of the combination can be calculated using the formula 1/f_combine = 1/f_1 + 1/f_2.
• The combination can have different characteristics based on the powers and orientations of the lenses. "

Slide 11:

Power of a Lens and Combination of Thin Lenses in Contact - Some examples on combination of thin lenses in contact

• Example 1:
  • Lens 1: Converging lens with power +2 D and focal length f_1 = 0.4 m.
  • Lens 2: Converging lens with power +3 D and focal length f_2 = 0.3 m.
  • Power of the combination: P_combine = P_1 + P_2 = +2 D + +3 D = +5 D.
  • Focal length of the combination: 1/f_combine = 1/f_1 + 1/f_2 = 1/0.4 + 1/0.3 = 2.5 + 3.33 = 5.83 m^(-1).
• Example 2:
  • Lens 1: Converging lens with power +4 D and focal length f_1 = 0.25 m.
  • Lens 2: Diverging lens with power -2 D and focal length f_2 = -0.5 m.
  • Power of the combination: P_combine = P_1 + P_2 = +4 D + (-2 D) = +2 D.
  • Focal length of the combination: 1/f_combine = 1/f_1 + 1/f_2 = 1/0.25 + 1/(-0.5) = 4 + (-2) = 2 m^(-1).

Slide 12:

Power of a Lens and Combination of Thin Lenses in Contact - Some examples on combination of thin lenses in contact

• Example 3:
  • Lens 1: Diverging lens with power -3 D and focal length f_1 = -0.4 m.
  • Lens 2: Diverging lens with power -2 D and focal length f_2 = -0.5 m.
  • Power of the combination: P_combine = P_1 + P_2 = -3 D + -2 D = -5 D.
  • Focal length of the combination: 1/f_combine = 1/f_1 + 1/f_2 = 1/(-0.4) + 1/(-0.5) = -2.5 + -2 = -4.5 m^(-1).
• Example 4:
  • Lens 1: Converging lens with power +3 D and focal length f_1 = 0.33 m.
  • Lens 2: Diverging lens with power -5 D and focal length f_2 = -0.2 m.
  • Power of the combination: P_combine = P_1 + P_2 = +3 D + (-5 D) = -2 D.
  • Focal length of the combination: 1/f_combine = 1/f_1 + 1/f_2 = 1/0.33 + 1/(-0.2) = 3.03 + (-5) = -1.97 m^(-1).

Slide 13:

Power of a Lens and Combination of Thin Lenses in Contact - Some examples on combination of thin lenses in contact

• Example 5:
  • Lens 1: Converging lens with power +1 D and focal length f_1 = 1 m.
  • Lens 2: Diverging lens with power -2 D and focal length f_2 = -0.5 m.
  • Power of the combination: P_combine = P_1 + P_2 = +1 D + (-2 D) = -1 D.
  • Focal length of the combination: 1/f_combine = 1/f_1 + 1/f_2 = 1/1 + 1/(-0.5) = 1 - 2 = -1 m^(-1).
• Example 6:
  • Lens 1: Diverging lens with power -4 D and focal length f_1 = -0.25 m.
  • Lens 2: Converging lens with power +3 D and focal length f_2 = 0.33 m.
  • Power of the combination: P_combine = P_1 + P_2 = -4 D + +3 D = -1 D.
  • Focal length of the combination: 1/f_combine = 1/f_1 + 1/f_2 = 1/(-0.25) + 1/0.33 = -4 + 3.03 = -0.97 m^(-1).

Slide 14:

Summary and Key Points

• Combination of thin lenses in contact can yield different powers and focal lengths depending on the characteristics of the individual lenses.
• The power of the combination is the sum of the powers of the individual lenses.
• If both lenses have the same power, the power of the combination doubles.
• The focal length of the combination can be calculated using the formula 1/f_combine = 1/f_1 + 1/f_2.
• In some cases, the combination can result in a converging lens, a diverging lens, or even a combination with zero power.

Slide 15:

Applications of Combination of Thin Lenses in Contact

• Camera lenses: Combination of lenses is used to adjust the focus, zoom, and image quality in cameras.
• Binoculars/Telescopes: Combination of lenses helps in magnification and clear vision of distant objects.
• Microscopes: Combination of lenses provides magnification and resolution to observe microscopic objects.
• Eyeglasses/Contact lenses: Combination of lenses corrects vision problems such as myopia (near-sightedness) and hyperopia (far-sightedness).

Slide 16:

Real-Life Examples - Camera Lenses

• Camera lenses consist of a combination of multiple lenses in contact.
• Different lenses are used to adjust the focus, zoom, and image quality.
• The combination of lenses allows the camera to capture sharp and clear images.
• Wide-angle lenses, telephoto lenses, and macro lenses are popular examples of combination lenses.

Slide 17:

Real-Life Examples - Binoculars/Telescopes

• Binoculars and telescopes use a combination of lenses to magnify distant objects.
• The combination of lenses helps in focusing the light from the objects and bringing them into sharp focus.
• High-quality binoculars and telescopes often have multiple lens elements to enhance the image quality and reduce aberrations.

Slide 18:

Real-Life Examples - Microscopes

• Microscopes use a combination of lenses to observe microscopic objects.
• The combination of lenses provides magnification and resolution, allowing scientists to study cell structures and microorganisms.
• Compound microscopes typically have two lens systems - the objective lens and the eyepiece lens - working together to produce highly magnified images.

Slide 19:

Real-Life Examples - Eyeglasses/Contact Lenses

• Eyeglasses and contact lenses correct vision problems using a combination of lenses.
• Convex lenses are used to correct myopia (near-sightedness) by diverging the incoming light.
• Concave lenses are used to correct hyperopia (far-sightedness) by converging the incoming light.
• The combination of lenses ensures that the light entering the eyes focuses correctly on the retina, providing clear vision.

Slide 20:

Summary and Key Points

• Combination of thin lenses is used in various real-life applications, including camera lenses, binoculars/telescopes, microscopes, and eyeglasses/contact lenses.
• These combinations of lenses allow for image magnification, focus adjustment, and vision correction.
• Understanding the power and focal length of the combination is essential for optimizing the performance of these devices.
• The formula 1/f_combine = 1/f_1 + 1/f_2 is used to calculate the focal length of the combination of lenses.
• Practical examples demonstrate the principles and applications of the combination of thin lenses in contact.

Slide 21:

• Example 1:
  • Lens 1: Diverging lens with power -2 D and focal length f_1 = -0.5 m.
  • Lens 2: Diverging lens with power -5 D and focal length f_2 = -0.2 m.
  • Power of the combination: P_combine = P_1 + P_2 = -2 D + -5 D = -7 D.
  • Focal length of the combination: 1/f_combine = 1/f_1 + 1/f_2 = 1/(-0.5) + 1/(-0.2) = -2 + -5 = -7 m^(-1).
• Example 2:
  • Lens 1: Diverging lens with power -3 D and focal length f_1 = -0.33 m.
  • Lens 2: Converging lens with power +5 D and focal length f_2 = 0.2 m.
  • Power of the combination: P_combine = P_1 + P_2 = -3 D + +5 D = +2 D.
  • Focal length of the combination: 1/f_combine = 1/f_1 + 1/f_2 = 1/(-0.33) + 1/0.2 = -3.03 + 5 = 1.97 m^(-1).

Slide 22:

• Example 3:
  • Lens 1: Diverging lens with power -4 D and focal length f_1 = -0.25 m.
  • Lens 2: Diverging lens with power -1 D and focal length f_2 = -1 m.
  • Power of the combination: P_combine = P_1 + P_2 = -4 D + -1 D = -5 D.
  • Focal length of the combination: 1/f_combine = 1/f_1 + 1/f_2 = 1/(-0.25) + 1/(-1) = -4 + -1 = -5 m^(-1).
• Example 4:
  • Lens 1: Converging lens with power +3 D and focal length f_1 = 0.33 m.
  • Lens 2: Converging lens with power +1 D and focal length f_2 = 1 m.
  • Power of the combination: P_combine = P_1 + P_2 = +3 D + +1 D = +4 D.
  • Focal length of the combination: 1/f_combine = 1/f_1 + 1/f_2 = 1/0.33 + 1/1 = 3.03 + 1 = 4.03 m^(-1).

Slide 23:

• Example 5:
  • Lens 1: Diverging lens with power -1 D and focal length f_1 = -1 m.
  • Lens 2: Converging lens with power +2 D and focal length f_2 = 0.5 m.
  • Power of the combination: P_combine = P_1 + P_2 = -1 D + +2 D = +1 D.
  • Focal length of the combination: 1/f_combine = 1/f_1 + 1/f_2 = 1/(-1) + 1/0.5 = -1 + 2 = 1 m^(-1).
• Example 6:
  • Lens 1: Converging lens with power +4 D and focal length f_1 = 0.25 m.
  • Lens 2: Diverging lens with power -3 D and focal length f_2 = -0.33 m.
  • Power of the combination: P_combine = P_1 + P_2 = +4 D + -3 D = +1 D.
  • Focal length of the combination: 1/f_combine = 1/f_1 + 1/f_2 = 1/0.25 + 1/(-0.33) = 4 + (-3.03) = 0.97 m^(-1).

Slide 24:

Summary and Key Points

• Combination of thin lenses in contact can yield different powers and focal lengths depending on the characteristics of the individual lenses.
• The power of the combination is the sum of the powers of the individual lenses.
• If both lenses have the same power, the power of the combination doubles.
• The focal length of the combination can be calculated using the formula 1/f_combine = 1/f_1 + 1/f_2.
• In some cases, the combination can result in a converging lens, a diverging lens, or even a combination with zero power.

Slide 25:

Applications of Combination of Thin Lenses in Contact

• Camera lenses: Combination of lenses is used to adjust the focus, zoom, and image quality in cameras.
• Binoculars/Telescopes: Combination of lenses helps in magnification and clear vision of distant objects.
• Microscopes: Combination of lenses provides magnification and resolution to observe microscopic objects.
• Eyeglasses/Contact lenses: Combination of lenses corrects vision problems such as myopia (near-sightedness) and hyperopia (far-sightedness).

Slide 26:

Real-Life Examples - Camera Lenses

• Camera lenses consist of a combination of multiple lenses in contact.
• Different lenses are used to adjust the focus, zoom, and image quality.
• The combination of lenses allows the camera to capture sharp and clear images.
• Wide-angle lenses, telephoto lenses, and macro lenses are popular examples of combination lenses.

Slide 27:

Real-Life Examples - Binoculars/Telescopes

• Bin