Question

Draw a ray diagram to show the image formation by a combination of two thin convex lenses to contact. Obtain the expression for the power of this combination in terms of the focal lengths of the lenses.

Answer 1

In the above diagram,$L_{1}and{L}_2$ are two convex lenses, O be the point object and $I_{1}and{I}_2$ are the images obtained by the lens $L_1$ and $L_2.$

Let $P_1$ and $P_2$ are the power of the lenses, and $f_{1}and{f}_2$ are the focus length of the two lenses then,

$\frac{1}{f_1}=\frac{1}{v_1}-\frac{1}{u}----------\left(1\right)$

$\frac{1}{f_2}=\frac{1}{v}-\frac{1}{v_1}----------\left(2\right)$

By adding the equation (1) and (2)

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f_1}+\frac{1}{f_2}$

So, We know that ,

$P=\frac{1}{f}$

So $P=\frac{1}{f_1}+\frac{1}{f_2}$

Then, $P=P_1+P_2$.