Consider two thin lenses, M and N having focal lengths of and , respectively. They are kept in…
Physics20263 marksDerivation
Consider two thin lenses, M and N having focal lengths of $f_{1}$ and $f_{2}$, respectively. They are kept in contact with each other as shown in Figure 6 below. A point object 'S' is kept on the common principal axis. The first lens M forms an image at $I_{1}$, which serves as a virtual object for the second lens N. The final image formed by the combination is 'I'.
Given: Two thin lenses M and N of focal lengths $f_1$ and $f_2$ in contact
To show: $\frac{1}{F} = \frac{1}{f_1} + \frac{1}{f_2}$
Figure 6
(i)[2.0]
Apply the lens formula for the formation of:
(a) Image $I_{1}$ by the first lens M.
(b) Image I by the second lens N.
(ii)[1.0]
Hence, obtain an expression for equivalent focal length (F) in terms of $f_{1}$ and $f_{2}$.
