Comprehensive Notes on Lenses

Lenses

Introduction to Lenses

• Doubt and observation are key to learning about lenses.
• Older people use reading lenses to magnify letters.
• Lenses are used in:
  • Toys
  • Spectacles
  • Door lenses
• Telescopes use lenses to make distant objects appear closer and more distinct.
• Lenses differ from glass sheets in their properties.

Convex Lenses

• A thin sheet of glass does not change the size of the illuminated part when sunlight falls on it.
• A convex lens, when held at a specific distance from the paper, reduces the size of the illuminated area and increases the intensity of light, potentially causing the paper to smolder and catch fire as shown in Figure 2.2.
• Convex Lenses are thicker in the middle and magnify objects.
• Convex lenses converge light rays.

Concave Lenses

• Concave lenses are thinner in the middle (Fig 2.4).
• Concave lenses cannot converge light rays.

Characteristics Comparison

• Convex Lens:
  • Thicker in the middle
• Concave Lens:
  • Thicker at the edges

Distinguishing Lenses

• When a convex lens is used, letters appear to move in the opposite direction.
• This activity can distinguish between convex and concave lenses.
• Lenses have two refracting surfaces (Fig 2.5 (a) and 2.5 (b)).
• Refracting surfaces of a lens are parts of spheres.
• A lens is a transparent medium where each refracting surface is part of a sphere.

Terms Related to Lenses

• Optic Centre (O):
  • The midpoint of a lens.
• Centres of Curvature (C1, C2):
  • Each refracting surface of a lens is part of a sphere; the centers of these spheres are the centers of curvature (Figures 2.6 and 2.8).
• Optic Axis:
  • The imaginary line passing through the centers of curvature and the optic center of a lens.
• Aperture:
  • The area of the lens through which light passes.
  • In optical instruments like cameras and microscopes, the aperture can be varied using a stop.

Experiment to find principal foci of lenses:

• Materials:
  • Box (50 cm length, 30 cm width, 20 cm height), transparent on one side
  • Small hole on opposite sides of box sealed with transparent sheet
  • Laser torch (high beam type)
  • Incense stick
  • Match box
  • Convex lens
  • Concave lens
  • Lens stand
• Procedure:
  • Fix convex lens on the stand inside the box and fill the box with smoke.
  • Allow light rays from laser torch to pass through hole and fall on the lens.

Principal Focus of Convex Lens

• Light rays parallel to the optic axis of a convex lens converge to a point on the other side of the lens after refraction.
• This point is the principal focus (F) of the convex lens.
• Convex lenses have two principal foci, one on each side of the lens, equidistant from the optic center.
• The principal focus of a convex lens is considered real because light rays passing parallel to the optic axis pass through the principal focus after refraction.

Focal Length

• The focal length $(f)$ is the distance from the optic center of the lens to the principal focus (Fig 2.9).

Approximate Focal Length

• To find the approximate focal length of a convex lens, use the distant object method.
• Project the image of a distant tree or building onto a screen using a convex lens.
• Measure the distance between the lens and the image using a scale; this distance is the approximate focal length of that lens.

Principal Focus of Concave Lens

• Light rays, near and parallel to the optic axis incident on a concave lens, after refraction appear to diverge from a point on the optic axis on the same side of the lens.
• This point is the principal focus of a concave lens (F).
• A concave lens also has two principal foci.
• The principal focus of a concave lens is considered virtual because refracted rays do not pass through the principal focus of a concave lens.

Image Formation by Lenses

• Real images can be projected on a screen.
• Experiment: Project the image of a window onto a screen using a convex lens.
• It is not possible to form an image on the screen using a concave lens.
• A concave lens diverges the rays of light.

Examples of Real Images

• Image captured on a camera.
• Image formed on a cinema screen.

Image Formation by a Convex Lens

• Ray diagrams are used to illustrate the path of light rays from an object placed in front of a convex lens as they pass through the lens.
• The position and characteristics of the image vary based on the object's position (Table 2.2).

Image Position and Characteristics Based on Object Position

• Object Beyond 2F:
  • Image Position: Between F and 2F
  • Image Characteristics: Diminished, Inverted, Real
• Object at 2F:
  • Image Position: At 2F
  • Image Characteristics: (Not specified in the text, but implied: Same size, Inverted, Real)
• Object Between F and 2F:
  • Image Position: Beyond 2F
  • Image Characteristics: Magnified, Inverted, Real
• Object at F:
  • Image Position: At infinity (Far away)
  • Image Characteristics: (Not specified in the text, but implied: Highly magnified, Inverted, Real)
• Object Between F and Lens:
  • Image Position: On the same side of the object
  • Image Characteristics: Magnified, Erect, Virtual

Properties of Light Rays Passing Through a Convex Lens

• A ray of light from a point which is parallel to the optic axis incident on a convex lens passes through the principal focus on the other side.
• A ray of light passing through the optic center goes straight without deviation.
• A ray of light after passing through the focus on the same side of the object incident on the lens becomes parallel to the optic axis after refraction.

Experiment

• Arrange a light source, the convex lens with pre-determined focal length, the lens stand and the screen.
• Measure and mark F and 2F on the experiment table on both sides of the lens.
• First place the object (light source) beyond 2F and adjust the position of the screen to get a clear image.
• Observe the features of the image and record them.

Observation

• When the object is beyond 2F, the image is between F and 2F on the other side, inverted, diminished and real.

Key Concept

• Light rays which have taken different paths pass through a single point and the image of A is formed at D. The image of any point on the object is formed at the point of convergence of refracted light rays originating from the corresponding points. If a screen is placed at the point of convergence of the refracted rays, the image is formed there.

Ray Diagrams

• Object at 2F
  • Position of the Image:
  • Characteristics of the Image:
• Object Between F and 2F
  • Position of the Image:
  • Characteristics of the Image:
• Object at F
  • Refracted rays do not converge.
  • Characteristics of the Image: (Not specified in the text, but implied: Highly magnified, Inverted, Real)
• A convex lens does not always form only real images.

Object Between F and the Lens

• Position of the image: On the same side of the object
• Characteristics of the image:
  • Erect
  • Virtual
  • Magnified

Image Formation by a Concave Lens

• It is not possible to form an image on the screen using a concave lens as it forms a virtual image.
• Table 2.4: Change in the path of light as it passes through a concave lens.

Properties of Light Rays Passing Through a Concave Lens

• Rays of light parallel to the optic axis incident on a concave lens appear to diverge after refraction.
• Light rays passing through the lens directed towards the principal focus on the other side appear to become parallel to the optic axis after refraction.
• Rays of light passing through the optic center go straight without deviation.

Object between F and 2F

• Position of the image:
• Characteristics of the image:

Object between F and Lens

• Position of the image:
• Characteristics of the image:

Summary of Image Formation by a Concave Lens

*Based on the image formation by a concave lens.

Key Observation

• The image formed by a concave lens is virtual.
• Concave lens diverges light rays, the image it forms is always virtual.
• The position of the image is always between F and the lens on the same side of the object.

Lens Equation and Distances

• Focal length: Distance from the optic center to the principal focus.
• Object distance: Distance from the optic center to the object.
• Image distance: Distance from the optic center to the image.
• These distances are used in the lens equation to calculate how far the image from the lens will be if an object is placed at a given distance.