A point object O on the principle axis of a spherical surface of radius of curvature R separating two media of refractive indices and
forms an image
as shown in the figure.
Prove that
(b) Use this expression to derive lens maker's formula. Draw the necessary diagrams.
(c) A convex lens is placed over a plane mirror. A pin is now positioned so that there is no parallax between the pin and its image formed by this lens-mirror combination. How will you use this observation to find focal length of the lens? Explain briefly.
Consider a spherical surface with center of curvature at C and radius of curvature R.
i is very small and the curved portion considered is the part of a large circle
From
From
From
Since the angle is very small
From Snells law
From (5) , (6) and (4)
Or
(b) A spherical lens can be considered as a two spherical surface. The image of the left surface act as a virtual object for the other surface.
For surface ABC
Apply equation (7) for surface
For surface
act as a virtual object for
(From (7))
For thin lens
Suppose the object is at infinity
is the lens makers formula
(c)
The rays after refraction from the lens fall normally to the mirror. So the rays will retrace their path, which implies that rays is originating from the focus, so the focal length equals the distance of pin from the mirror.