Note on Image Formed by Lenses

  • Note
  • Things to remember

A lens is an object, usually made of glass, bounded by one by two spherical surface. There are two types of lenses:

  1. Convex or converging lens
  2. Concave or diverging lens
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A concave lens is thick at the thin centre and thin at the edges while a concave lens is thin at the centre and thick at the edges. A convex lens causes parallel rays of light to converge after refraction but the concave lens does the opposite. There are different types of lenses, shown in the figure.

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Some related terms

  1. Center of curvature:
    The centre of the sphere of which lens forms a part is called the centre of curvature. A lens has two centres of curvature C1 and C2.
  2. Radius of curvature:
    The radius of the sphere whose parts form a lens is known as the radius of curvature. A lens consists of two radii of curvature R1 and R2 which may be equal.
  3. Optical centre:
    The geometrical centre of the lens is known as an optical centre. Here 'o' is the optical centre.
  4. Principal focus:
    When a parallel beam of light incident on a lens after refraction, it appears to meet from a point or it meet at a point. That point is called principal focus.
    Note:Principal focus is real for the convex lens and virtual for the concave lens.
  5. Principal axis:
    The line passing through the centre of curvature of both spheres is called principal axis.
  6. Focal length:
    The distance between the optical centre and principal focus is called focal length.
  7. Focal plane:
    the plane passing through the focus and perpendicular to the principle axis of a lens is called the focal plane.
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Image Formed by Lenses

Ray diagram are useful in locating the images formed by lenses. Any two of the following principle rays are sufficient to locate the image produced by the lens.

  1. A ray passing through optical centre of the lens passes without deviation.
  2. A ray parallel to the axis passes through the focus after refraction.
  3. A ray passing through focus emerges parallel to the axis after refraction.

Image Formed by Convex Lens

  1. When object lies at infinity
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    In this case, image will be formed in next side of the object at focus F which is real, inverted and point in size.
  2. When object lies beyond 2F
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    In this case, image will be formed between F and 2F in the next side of the object which is real, inverted and smaller in size.
  3. When object lies at 2F
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    In this case, image will be formed on next side of the object at 2F which is real, inverted and equal in size.
  4. When object lies between F and 2F
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    In this case image will be formed in next side of object beyond 2F which is real, inverted and larger in size.
  5. When object lies at F
    a


    In this case, image will be formed on next side of object at infinity which is real, inverted and highly magnified,
  6. When object at F and O
    f


    In this case, image will be formed on the same side of the object which is virtual, erect and magnified.


Image Formed by a Concave Lens

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When an object lies at any point on principle axis, it’s image formed by concave lens lies in same side of object which is virtual, erect and smaller in size.

Table showing formation of Images by lenses:

Lens

Position of object

Position of image

Nature of image

Size of image

Convex

1. At infinity

, At focus

Real and inverted

Extremely small

2. Between infinity and 2f

Between infinity and 2f

Small

3. At 2F

At 2F

Real and inverted

Small size

4. Between 2F and F

Beyond 2F

Real and inverted

Magnified

5. At focus

At infinity

Real and inverted

Extremely large

6. Between focus and optical centre

On the side of object

Virtual and erect

Large

Concave

a. At infinity

At focus

Virtual and erect

Small

b. Between infinity and optical centre

Between focus and optical centre

Virtual and erect

Small

Action of a lens

A thin lens may be considered as made up of a large number of small angle prisms placed together. The refracting angle of these prisms, made by lens surfaces, increases from zero at the middle to a small value at the edges. The prism farther away from the middle deviates from zero an incident ray more than those prisms near the middle. A ray passing through the centre part of lens passes un deviated because it is a rectangular glass block. Such action of lens is shown in the figure.

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  • Center of curvature:
    The centre of the sphere of which lens forms a part is called the centre of curvature. A lens has two centres of curvature C1 and C2.
  • Radius of curvature:
    The radius of the sphere whose parts form a lens is known as the radius of curvature. A lens consists of two radii of curvature R1 and R2 which may be equal.
  • Optical centre:
    The geometrical centre of the lens is known as an optical centre. Here 'o' is the optical centre.
  • Principal focus:
    When a parallel beam of light incident on a lens after refraction, it appears to meet from a point or it meet at a point. That point is called principal focus.
    Note:Principal focus is real for the convex lens and virtual for the concave lens.
  • C
    The line passing through the centre of curvature of both spheres is called principal axis.
  • Focal length:
    The distance between the optical centre and principal focus is called focal length.
  • Focal plane:
    the plane passing through the focus and perpendicular to the principle axis of a lens is called the focal plane.
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