Question

A converging lens of focal length 40cm is kept in contact with a diverging lens of focal length 30cm. Find the length of the combination.

Answer 1

Hint: We will consider the focal lengths of both the lenses i.e. converging and the diverging lenses as per given in the question. Then we will add the focal lengths of both the mirrors by using the formula $\dfrac{1}{F} = \dfrac{1}{{{f_1}}} + \dfrac{1}{{{f_2}}}$ in order to have the combined length. Refer to the solution below.

Complete step-by-step answer:
Formula used: $\dfrac{1}{F} = \dfrac{1}{{{f_1}}} + \dfrac{1}{{{f_2}}}$

If the lens is biconvex or plano-convex, the lens converges on a point (a focus) behind the lens by means of a collimated light ray. The lens is called an optimistic or converging lens in this situation. With a thin in-air lens, the angle to the location from the lens is the focal length of the device, which in diagrams and calculations is normally f. An extended hemispheric lens is a particular plano-convex lens type, with a complete hemisphere in which the lens is bent and the lens is considerably broader than the curvature radius.

If the lens is biconcave, a collimated light stream that passes through the lens (spread) is diverged, therefore the lens is considered a negative or divergent lens. The pulse seems to emanate from a similar position on the horizon above the lens after going through the prism. With a thin lens in the sun, the focus range is the distance from that point to the eye, while the focal length of the convergent eye is adversely detrimental.

The focal length of the converging lens as per given in the question is 40cm (f1)

The focal length of the diverging lens as per given in the question is 30cm. it will have a negative sign as it is a concave lens (f2). Thus,

$
   \Rightarrow {f_1} = 40cm \\
    \\
   \Rightarrow {f_2} = - 30cm \\
$

The focal length of the entire combination (F) will be-

$
   \Rightarrow \dfrac{1}{F} = \dfrac{1}{{{f_1}}} + \dfrac{1}{{{f_2}}} \\
    \\
   \Rightarrow \dfrac{1}{F} = \dfrac{1}{{40}} + \dfrac{1}{{\left( { - 30} \right)}} \\
    \\
   \Rightarrow \dfrac{1}{F} = \dfrac{1}{{40}} - \dfrac{1}{{30}} \\
    \\
   \Rightarrow \dfrac{1}{F} = \dfrac{{30 - 40}}{{1200}} \\
    \\
   \Rightarrow \dfrac{1}{F} = - \dfrac{{10}}{{1200}} \\
    \\
   \Rightarrow \dfrac{1}{F} = - \dfrac{1}{{120}} \\
    \\
   \Rightarrow F = - 120cm \\
$

Note: A lens is an optical transmission that concentrates or spreads a light beam by refraction. A single piece of translucent glass consists of a single lens, while a compound lens consists of multiple basic lenses (elements) normally organized around a specific axis. Lenses are constructed of glass or acrylic materials that are molded that are painted or shaped to the ideal form. Unlike a prism that refracts light without concentration, a lens can concentrate light in an image.