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Refraction by Spherical Lenses

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Refraction by Spherical Lenses - Lesson Summary


         Lenses are the most used things in optical devices like microscopes and telescopes. Bi-convex and bi-concave lenses are the most popular ones in use among school labs. Lenses use the phenomenon of refraction of light to form images.

Concave lens diverge the light incident on it. Hence, called the diverging lens. Due to this these lenses always form diminished, virtual and erect images irrespective of the position of the object in front of them. Thus, the magnification produced by these lenses is always less than one.

Convex lenses converge the light and hence are called the converging lenses. You can observe the magnified image of your palm when the lens is placed close to your palm. This is due the position of the object between the focus and the optic centre. As the object moves away from the lens, the size of its image reduces along with its distance from the lens. Convex lenses form erect, virtual, magnified images or inverted, real, diminished/magnified images depending on the position of the object.

Lens
A lens is a piece of transparent optical material with one or two curved surfaces to refract light rays.
It may converge or diverge light rays to form an image.

A bi-convex lens is one with a surface that is bulged outwards on both the sides. It is generally referred to as a convex lens.

Another type of a lens is a bi-concave lens that has two inward bent surfaces. It is generally referred to as a concave lens. 

A Plano-convex lens has a convex surface on one side and a plane surface on the other.

A Plano-concave lens is the one that has a concave surface on one side and a plane surface on the other.

A concavo-convex lens has a concave surface on one side and a convex surface on the other.

Convex and concave lenses are important as they are more commonly used than the other types of lenses.

Terms Used for Lens
Centre of Curvature:
The centre of the imaginary glass sphere of which the lens is a part, is called centre of curvature.

Principal Axis: An imaginary line joining the centres of curvature of the two spheres, of which lens is a part, is called Principal Axis.

Optical Centre: A point within the lens, where a line drawn through the diameter of lens meets principal axis, is called optical centre.

Principal Focus for Convex Lens: It is a point on the principal axis of a concex lens,  where parallel beam of light rays, travelling parallel to principal axis, after passing through the lens actually meet.

Principal Focus for Concave Lens: It is a point on the principal axis of a concave lens, from where parallel beam of light rays, travelling parallel to principal axis, after passing through the lens, appears to come.

Focal Length: The distance between principal focus and optical centre is called focal length.
Aperture: The effective diameter of the lens through which refration takes place is called aperture of lens.

Optic centre is a point on the axis of a lens such that any light ray passing through this point emerges without refraction.
      •  Principal focus is a point on the axis of a lens.
      •  Principal focus is also known as the focal point.  

Convex Lens
      •  A lens in which both the surfaces are convex, is known as convex lens
      •  Light rays incident on a convex lens get converged at its focus
      •  Used by palmists and fingerprint experts
      •  If an incident ray passes through a focus and its emergent ray passes parallel to the principal axis, then that focus is called the first principal focus.
      •  If an incident ray passes parallel to the principal axis, and its emergent ray converges at a focus, then that focus is called the second principal focus.
      •  The distance between the optic centre and the focal point is called the focal length.  

Behaviour of Light Rays Propagating Through a Convex Lens                  Incident Ray                      Emergent Ray Is parallel to principal axis Passes through focus Passes through optic centre Passes with out deviation passes through focus Passes parallel to principal axis
Location and Characteristics of Images Formed by a Convex Lens
     Object Location               Image Location          Nature of Image Infinity At F2 Real
Inverted
Highly Diminished Beyond 2F1 Between F2 and 2F2 Real
Inverted
Diminished At 2F1 At 2F2 Real
Inverted
Equal in size to that of the object Between 2F1 and F1 Beyond 2F2 Real
Inverted
Magnified At F1 Infinity Real
Inverted
Highly Magnified Between F1 and O On the same side of lens as the object Virtual
Erect
Magnified
Concave Lens 
A lens, in which both the surfaces are concave, is known as a concave lens.
 
An image formed by a concave lens is always diminished due to the divergence of rays. This is why concave lenses are widely used to correct eye defects such as myopia.
 
A concave lens is also known as a diverging, reducing, negative and myopic or minus lens.
 
Behaviour of Light Rays Propagating Through a Concave Lens           Incident Ray           Emergent Ray Is parallel to principal axis Appears to pass through focus Passes through optic centre Passes without deviation Is directed towards focus Passes parallel to principal axis
The lens formula defines the relationship between the focal length of the lens (f), the distance of the object from the optic centre (u) and the distance of the image from the optic centre (v):
  1 f   = 1 v - 1 u
Where,
     f = focal length
    u = object distance
     v = image distance
 
Location and Characteristic of the Images Formed by a Concave Lens            Object Location       Image Location    Nature of Image   Infinity  As a point at F1 Virtual
Erect
Highly Diminished   Beyond 2F1  Between F1 and O Virtual
Erect
Diminished

Sign convention for spherical lenses:

  • All distances measured above the principal axis are taken as positive. Thus, height of an object and that of an erect image are positive and all distances measured below the principal axis are taken as negative.

  • The distances measured in the direction of incident rays are taken as positive and all the distances measured in the direction opposite to that of the incident rays are taken as negative.

  • All distances on the principal axis are measured from the optic center.


Lens Formula and Sign Conventions

1 f = 1 v - 1 u
Where,
     f = focal length
    u = object distance
     v = image distance
 
All the distances are to be measured from the optic centre of the lens:
 
The distances measured in the direction of the incident light are taken as positive (+).
The distances measured in the direction opposite to that of the incident light are taken as negative (-).
 
Magnification (m)
Magnification is the ratio of the image size to the object size. It is also measured as the ratio of image distance to object distance.

 m = (Size of the image / Size of Object ) Or m = (Image distance / Object distance)

If m = 1;  image size = object size
If m > 1:  image size > object size
If m < 1:  image size < object size
 
Power of Lens (P)
      •  The converging or diverging capacity of a lens is ascertained by its power
      •  Power of a lens is the reciprocal of its focal length expressed in metre. P =  1 f  ( measured in meters) .
      •  SI Unit of power of a lens is dioptre (D).
      •  Power of a convex lens is positive and that of a concave lens is negative.

Differences Between Convex Lens and Concave Lens              Convex Lens               Concave Lens 1.  It is thick in the middle and thin at the edges.
2.  It converges the incident rays towards the principal axis.
3. It has a real focus. 1.  It is thin in the middle and thick at the edges.
2. It diverges the incident rays away from the principal axis.
3. It has a virtual focus.

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