Lens is a portion of refracting medium bounded by one or two spherical surfaces, that is, two surfaces may be curved or one curved surface and another plane surface. Lenses are divided into two types. They are:-

  • Convex lens and
  • Concave lens

Convex lens is called a converging lens because after passing through this lens, the emergent rays come closer to one another. A parallel incident rays meets or converges at its focus.
Concave lens is called a diverging lens because after refraction through this lens, the emergent rays go further apart from one another. A parallel incident rays appeared to diverge from its focus.
The differences between convex and concave lens are:
Convex lens Concave lens
a) It is thick at the middle and thin at the edges. a) It is thick at the edges and thin at the middle.
b) It converges all parallel rays of light falling on its surface at a point. b) It diverges all parallel rays of light falling on its surface away from a point.
c) Depending upon the object distance, the image may be real or virtual, magnified or diminished and erect or inverted. c) It always forms the image which is virtual, erect and diminished.
The ability of a lens to converge or to diverge rays of light is called the power of lens. In other words, the reciprocal of the focal length of a lens is called power of lens. It is denoted by the letter "p". The unit of power of lens is diopter (D).
The distance between the optical center and the principal focus of a lens is called focal length. It is denoted by f.
The three uses of the lens are as follows:
  1. They are used as spectacles.
  2. They are used in telescope, camera, slide projector, etc.
  3. Convex lens having short focal length is used as magnifying glass.
A lens is a denser medium than air. Hence, the light rays refract from lens when the light rays passes from lens. The refraction occurs due to change in speed of light in medium.
In other word, when light travels from air to lens medium, due to changes in speed, the light rays are refracted.
  1. Center of curvature: it is the center of the sphere of which the lens forms a part. A lens has two centers of curvatures, which are denoted by C1 and C2.
  2. Principal axis: The line passing through the two centers of curvature of is known as principal axis.
  3. Optical center: The geometrical center of a lens is called its optical center. A ray of light passing through it does not bend even after refraction. It is denoted by "O".
  4. Principal focus: When narrow parallel rays of light fall on the surface of lens parallel and close to the principal axis, the rays of light converge to a point or appear to come from a point after refraction. The point is known as principal focus. It is denoted by "F".
  5. Focal length: The distance between principal focus (F) and optical center (O) is known as focal length. It is denoted by "f". It is taken as positive (+ve) for convex lens and negative (-ve) for concave lens.
The image formed is virtual and magnified when the object is placed within its focal length, so convex lens can be used as magnifying lens.
The main uses of convex lens are as follows:
  1. It is used to correct the defects of vision of eyes called long-sightedness.
  2. It is used to make simple microscope, compound microscope, camera and telescope, etc.
  3. It is used to make the paper burn from sunlight.
The main uses of concave lens are as follows:
  1. It is used to correct the defects of vision of eyes called short-sightedness.
  2. It is used to combine with convex lens to get clear image on camera, telescope, microscope, etc.
The power of lens is called one dioptre, if the focal length of a lens is one meter.
The ration between size of the image formed to the size of the object is called magnification. The magnification is generally represented by letter "M".

In other words, the magnification can be defined as the ratio between the image distance to object distance.
  1. Real, inverted and diminished - Convex lens between 2F and infinity)
  2. Virtual, upright and diminished - Concave lens (between optical center and infinity)
  3. Virtual, upright and enlarged - Convex lens (between F and optical center)
Here,
We have,
or, or,= 1m
f = 1m
This type of lens must be convex in nature.

Solution,
Here,
Power of lens (P) = +2D
Focal length (f) = ?
Now using formula,

or,
or, = 0.5m
f = 0.5m
Hence, the focal length of the lens is 0.5m (50 cm).
Here, the power of lens is positive i.e. the lens is convex lens.
So, the man is suffering from the long-sightedness or hypermetropia.

Solution,
Here,
Focal length (f) = 25cm = 0.25m
Power of lens (P) = ?
We know that,

or, = 4D
or, P = 4D Hence, the power of lens is 4 dioptre.