Generally, a convex lens can converge a beam of parallel rays to a point on the other side of the lens. This point is called a focus of the lens and its distance from the Optical Center of the beam is called the focal length. The radius of curvatures R1 and R2 of the spherical surfaces and the focal length of the lens ‘f’ are connected by an approximate equation.

For Mathematical Equation:

Where, n is the refractive index .

R1 and R2 are the radii of curvature.

R1 is denoted as the surface very near to the light source.

R2 is denoted as the surface very far from the light source.

In the case of Double Convex Lens, the focal length is greater due to the presence of the second curved surface. Since many optical devices require longer focal lengths then Double Convex Lenses are more preferred.

( Diagram of convex lens)

Formula:

Where, f is focal length

v is denoted as the distance of the image from the optical center.

u is denoted as the distance of the object from the optical center

In convex lens, the focal length is positive.

There are following uses:

A convex lens is called a converging lens because it converges a parallel beam of light on a point called the principal focus.

It is a ratio between the image height and object height. A magnification of 2 indicates the image is twice the size of the object and a magnification of 1 indicates an image size being the same as the object size. If the magnification is positive, then the image is upright compared to the object (virtual image). If magnification is negative then the image is inverted as compared to the object (real image).

2. When the object is beyond the Imaginary point then an image is formed between the Focal point and an imaginary point which is real, inverted and diminished.

3. When the object is an imaginary point, then an image is formed at an imaginary point which is the real, inverted and of the same size.

4. When the object is between the Focal point and the imaginary point then an image is formed beyond an imaginary point which is real, inverted and magnified.

5. When the object is at Focal point then an image is at infinity which is real inverted and magnified.

6. When the object is between the Focal point and the Centre of curvature then the image is formed beyond the imaginary point and behind the object which is virtual and magnified.

The focal length (f) = 18cm

The focal length is positive that is a convex lens. Then the focal point is real or the rays pass through the point.

The object height (ho) = 6 cm

The object distance (do) = 6 cm

Formation of an image by the convex lens:

The image distance (di):

1/di = 1/f – 1/do = 1/18 – 1/6 = 1/18 – 3/18 = -2/18

di = -18/2 = -9 cm

The negative sign denoted as the image is virtual or the rays do not pass through the image.

The magnification of image (m):

m = – di / do = -(-9)/6= 9/6 = 1.5

The positive sign denotes upright image.

The image height (hi):

m = hi / ho

hi = m ho = (1.5)6=9cm

The positive sign denotes that the image is upright.

The properties of the image:

1. It is virtual.

2. It is upright.

3. The image is greater than the object.

4. The image distance is greater than the object distance.