Biconvex Lens

Biconvex lenses are a type of simple lens. It has a wide area of applications like controlling and focusing of laser beams, image quality and other use in optical instruments. It is also called a plano-convex lens. Here, a parallel beam of light passes through the lens and converges into a focus or spot behind the lens. Thus, the biconvex lens is also called the positive and converging lens. The distance from the lens to the spot behind the lens is called the focal length of the lens. There are two curvatures on both sides of the lens which will be around 2 focal points and 2 centres. There is a line called the principal axis which is drawn on the middle of the biconvex lens.  These lenses are symmetrical lenses which have two convex lenses arranged in a spherical form. Each of these lenses has the same radius of curvature.

Images that are formed by the lenses are due to refraction of light. The convex lens is also known as the converging lens as it converges the rays coming towards its direction at a certain point. The image formed is thus, real. Thus, biconvex lenses have a wide range of usage in the optical industries and it has allowed us to capture images making it easier and more accessible. 

We know that images formed by lenses are because of the reflection of light. A convex lens is a converging lens that converges the rays coming from the point object at a certain point; therefore, the image formed is real.

We know that the centre of the spherical convex lens is the optical centre. When the two spheres intersect each other in such a way that their optical centres coincide; this type of arrangement is called the biconvex lens.

Focal Point of Biconvex Lenses

From Fig.1, we can see that the red point is the optical centres of two spherical convex lenses coinciding with each other. 

One thing to be noticed is that the distances PO1 and PO2 are equal. Here, O1 and O2 are the centres of curvatures of two convex lenses or biconvex lenses. 

Since O1 and O2 are the centres of curvatures, i.e., PO1 and PO2 are the radii of curvatures, so PO1 = PO2. This proves that biconvex lenses have the same radius of curvatures.

The line joining the centres of curvatures of these two lenses viz: O1and O2, passing via optical centre ‘P’ is the principal axis of the biconvex lenses.

We know that a convex lens contains two focal points one is on the left-hand side and the other on the right-hand side. 

The focal point lies in the centre (midpoint) of the line segment joining the optical centre and the centre of curvature. Since we are talking about biconvex, there will be two focal points viz: f1 and f2. We call these focal points the principal focus because this point lies on the principal axis.

So,

Pf1 = f1O1, so OC = 2f1. Similarly, Pf2 = f2O2, and therefore, PO2 = 2f2.

Biconvex Lens Formula

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We know that 

\[ \frac{1}{f}=\frac{1}{u}−\frac{1}{v} \]

We know that the general equation for the refraction on the spherical surface is given by:

\[ \frac{\mu_2}{v} - \frac{\mu_2}{u} = \frac{\mu_2 - \mu_1}{R} \]

Now, considering Fig. (2) to frame the biconvex lens formula:

After the first refraction, the image is formed at O1. So the equation becomes:

\[ \frac{\mu_{2}}{v} - \frac{\mu_{2}}{u} = \frac{\mu_2- \mu_1}{R_1} \]

After the second refraction, the image is formed at I. So the equation for the light ray coming from the medium \[μ_2\]  to the medium \[μ_1\]  is:

\[ \frac{\mu_2}{v} - \frac{\mu_1}{v_2} \] = \[ \frac{\mu_2 - \mu_1}{R_2} \] \[ \frac{\mu_2 - \mu_1}{R_1} \]

Adding eq (a) and (b), we get:

\[ \frac{1}{v} - \frac{1}{u} = \left ( \frac{\mu_2}{\mu_1} - 1 \right ) \left ( \frac{1}{R_1} - \frac{1}{R_2} \right ) \]

As the light rays come from the object placed at infinity, so u = ∞ and v = f.

So, from eq (1) and  (c), we get the biconvex lens formula as:

\[ \frac{1}{f} = \left ( \frac{\mu_2}{\mu_1} - 1 \right ) \left ( \frac{1}{R_1} - \frac{1}{R_2} \right ) \]

Here,

\[R_1\] = radius of curvature of lens 1

\[R_2\] = radius of curvature of lens 2

How to Make Biconvex Lenses?

• Take cardboard and cut out a circle of diameter 2.5 cm.

• Now, place this circle on the plastic water bottle. Draw its shape, and cut out two circles from the bottle with the help of scissors.

• Join these circles: 

             For joining these circles take a glue gun. Join their edges by leaving a space in :

             between these two, as shown in the image below

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• Take a bowl of water and let the joined circle dip into the water. We can see that some water fills in between the space of these two circles. Now, again stick the left space with glue.

• Now, take a handwritten notes register and read the sentences with the help of this lens. You will notice that word-to-word in each sentence will appear magnified.

Uses of Biconvex Lens

We use Biconvex lenses in our day-to-day life, as we discussed in the ‘how to make a biconvex lens’ section where this lens works as a magnifying glass to observe the small letters. Now, let’s see some more applications of biconvex lenses:

• We talk about many imaging systems like microscopes, telescopes, binoculars, projectors, etc; however, all these systems use biconvex lenses for obtaining images.  

A microscope uses biconvex lenses for imaging the things that are not visible to naked eye. For example, to determine the cellular structures of organs, germs, bacteria, and other microorganisms.

Telescopes use biconvex lenses to observe distant objects by their emission, electromagnetic radiations, and absorption. This helps to determine the temperature of the stars.

• We can use biconvex lenses as burning glasses.

• Biconvex lenses are found in the natural camera viz:  the human eye, where they produce virtual images.

• Biconvex lenses are positive lenses, and they are best-used for converging beams that are diverging in nature. 

• We find the applications of biconvex lens industries and also in image relays.