Geometrical Optics

on

Thin Lenses 





 

When the size of the physical and optical objects of a system are much larger than the wavelength of the light (or as λ→ 0 ), we are in the realm of geometrical optics. Optical systems in which the wave nature of light must be taken into account (interference, diffraction) are called physical optics. Of course, every real system experiences diffraction effects, so geometric optics is necessarily an approximation. However, the simplicity arising from treating only rays which move in straight lines affords many uses.

                                                      Fig: Concave and Convex Lens

A lens is a refracting device (a discontinuity in the medium) that redistributes the energy being propagated by electromagnetic radiation. This is usually achieved by re-shaping the wavefront, most usefully by turning spherical waves into plane waves and vice-versa.

Convex Lenses:
  • Lenses that cause an incoming plane wave to bend towards the axis through its middle are called converging or convex lenses. 
  • They are thicker at their midpoint than at their edges.

Concave Lenses:
  • Thicker at their edges than in the middle; they cause an incoming plane wave to bend away from its central axis and are hence also known as a diverging lenses. . 
 For converging lens, the point to which plane wave converges is called the focal point or focus.
 For diverging lens, it is point from which incoming spherical wave must emerge in order to produce plane wave upon passing through lens.

Simple lens has two refracting surface.

A lens is said to be thin lens, when thickness of lens is negligible with respect to its transverse diameter.

where n is refractive index, r1 and r2 are radius of curvature of lens surface.  f is focal length. i is image distance, o is object distance. M is magnification factor.

i > 0 , if  image is real
i < 0, if image is virtual

  DEFINITION: For a lens an image is virtual if it is formed on the side where the object is.
 DEFINITION: For a lens an image is real if it is formed on the opposite side of the lens.

With these sign conventions the same equations that we had for a mirror hold for a lens.

If medium of surrounding the lens is rarer and lens medium is denser.

Convex ( Converging)
  •  Image location - behind lens (if object distance >  focal length) , in front lens ( if object distance < focal length)
  • Image  - real ( if object distance  > focal length ) , virtual ( if object distance < focal length)
  • orientation - inverted ( if object distance  > focal length ), Erect (Same) ( if object distance < focal length)
  • sign of f is +ve
Concave ( Diverging )
  • Image location - infront of lens
  • Image  - virtual
  • orientation - Erect (Same) ( if object distance < focal length)
  • sign of f is  - ve
Ray Tracing

The three rays one can draw to and the object(remember one needs only two) are:
  1.  A ray that is initially parallel to the central axis of the lens will pass through the focal point behind the lens.
  2. A ray that passes through the focal point in front of the lens will emerge from the lens parallel to the central axis.
  3.  A ray that is initially derected toward the center of the lens wil emerge from the lens with no change in its direction.
NOTE: For ray tracing there is no substitute for seeing lots of ray tracing diagrams