• What could be the reasons for that difference?

    You might have noticed that in figures 4(a) and 4 (c) the refracted ray reaches a particular point on the principal axis. In figures 4(b) and 4(d) the refracted ray moves away from the principal axis. When you extend the refracted ray backwards along the ray as shown in 4b and 4d, the extended ray intersects the principal axis at some point. The point where refracted ray intersects the axis in all the above cases is called the focal point.

    You might have observed that a lemon in a glass of water appears bigger than its actual size, when viewed from the sides of tumbler.

• How can you explain this change in the size of lemon?

• Is the lemon that appears bigger in size an image of lemon or is it the real lemon?

• Can you draw a ray diagram to explain this phenomenon?

Let us find out.

      Consider a curved surface separating two media of refractive indices n1 and n2 ( figure 5). A point object is placed on the principal axis at point O. The ray, which travels along the principal axis passes through the pole undeviated. The second ray, which forms an angle α with principal axis, meets the interface (surface) at A. The angle of incidence is θ1 . The ray bends and passes through the second medium along the line AI. The angle of refraction is θ2 . The two refracted rays meet at I and the image is formed there.

Let the angle made by the second refracted ray with principal axis be γ and the angle between the normal and principal axis be β. (see fig.- 5)
In fig.- 5,
    PO is the object distance which we denote as ‘u’
    PI is image distance which we denote as ‘v’
  PC is radius of curvature which we denote as ‘R’
n1 , n2 are refractive indices of two media.
Can you establish any relation between the above mentioned quantities?
In the triangle ACO, θ1 = α + β