What is a Lens?
An optical tool or device that tends to both converge and diverge a beam of light (based on the situation and type) through refraction, is referred to as a lens.
A simple lens usually consists of only a single piece of transparent material whereas a compound lens tends to have several simple lenses (elements), that are generally arranged along a common axis.
What is Convex Lens?
The convex lens is a lens that converges rays of light that convey parallel to its principal axis (i.e. converges the incident rays towards the principal axis) which is relatively thick across the middle and thin at the lower and upper edges. The edges are curved outward rather than inward. It is used in front of the eye to bend the incoming light sharply so the focal point shortens and the light focuses properly on the retina.
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:
\[ \frac{1}{f} = (n–1)(\frac{1}{R_1} –\frac{1}{R_2})\]
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.
Focal Length:
This is the distance between the center of a convex lens where parallel rays converge.
Principal Axis:
A line passing through the center of the surface of a lens and through the centers of curvature of all segments of the lens.
For the Convex Lens, We Can Draw
A ray from the top of the object straight through the middle of the lens and its direction is not changed.
A ray from the top of the object parallel to the principal axis. It is refracted by the lens to pass through the focus
Formula:
\[ \frac{1}{f} =\frac{1}{v} + \frac{1}{u}\]
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 lenses, the focal length is positive.
Real Image and Virtual Image for Convex Lens
Real Image: A convex lens can be used to produce a real image, and this occurs if the object is located at a position of more than one focal length from the lens. It is projected in front of the lens and can be captured on a screen. It is used in movie theaters, projector etc.
Virtual Image: A convex lens will produce a virtual image if the object is located in front of the focal point. It is used in eyeglasses to give clear images.
Uses of the Convex Lens:
There are following uses:
It is used as Hypermetropia i.e., to correct far-sightedness.
It is used in microscopes, telescopes and magnifying glasses to subject all the light to a specific object.
It is used in camera lenses because they focus light for a clear picture.
It is used in front of the eye to bend the incoming light sharply so the focal point shortens and the light focuses properly on the retina.
It is also used in projectors, binoculars, optical microscopes, and even in the peep holes that are present in the doors of our houses.
Why is Convex Lens Called a Converging Lens?
A convex lens is called a converging lens because it converges a parallel beam of light on a point called the principal focus.
Images Formed By Convex Lens and Their Rules
When it comes to a convex lens, the image that is formed is always at such a point that at least two refracted light rays tend to meet on that point.
Here are the rules for obtaining an image formed by a convex lens:
Rule 1: A ray of light has to pass through the focus after refraction takes place through the lens. The ray of light must be originally parallel to the principal axis.
Rule 2: A ray of light that goes through the optical center of the convex lens will appear straight; it won’t bend after the refraction that takes place. And a ray of light that goes on the way of the principal axis of such a lens will also go in a straight direction; it won’t deviate either.
Rule 3: A ray of light will end up becoming parallel to the principal axis of a convex lens after refraction occurs through the lens when it passes through the focus of the lens.
Magnification of Convex Lens:
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).
Types of Convex Lens
1. Plano-convex Lens:
It is curved outwards from one side and the other side. It has positive focal length elements that have one spherical surface and one flat surface. These lenses are designed for infinite parallel light use in non-critical applications. These optical lenses are for all-purpose focusing elements. It is used in pharmaceuticals, defense, robots etc.
2. Double Convex Lens:
It is curved outwards from both sides. It is also known as the Biconvex lens or just convex. They have a shorter focal length than Plano-convex lenses of equal diameter and surface radius. So many optical devices require longer focal lengths. Hence, the double convex lenses are more preferred. It is used for the projector, monocular, Telescope, cameras etc. It produced the virtual image for the human eye and the real image for photography, an optical sensor and also used in burning glass
3. Concave-convex Lens:
It is curved inwards from one side and outwards from one side. It can be used to balance out the spherical aberrations caused by other lenses. It is used to control the laser beam. It is a combination of a lens with one convex lens and one concave lens side that is concave-convex lens or meniscus.
The Functions of the Convex Lens:
When the object is at infinity then a convex lens forms the image at focus which is real and inverted.
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.
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.
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.
When the object is at Focal point then an image is at infinity which is real inverted and magnified.
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.
Example:
A 6-cm high object is placed 6 cm from an 18-cm focal length. Find out the image distance, the magnification of the image, the image height and the properties of the image.
Solution:
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 an 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:
It is virtual.
It is upright.
The image is greater than the object.
The image distance is greater than the object distance.
Distinction Between Convex and Concave Lens
Interesting Facts About Convex Lens
The word lens has its root in Latin. It comes from the Latin name of “lentil” which is actually a plant. But it’s because a double-convex lens is more shaped like a lentil.
The word convex is defined as curving in an outward direction, like the rim of a circle. The shape of an eyeglass lens can be considered to be a good example of convexity.
One of the first scientists to use a small low telescope with a convex lens was Galileo. He did observe the moon and other celestial objects in the night sky.
A convex lens can be used as the main concentrator for multi-junction solar cells.
FAQs on Convex Lens
1. What is a convex lens and how does it differ from a concave lens?
A convex lens is a transparent optical device that is thicker in the middle than at the edges and converges parallel rays of light to a single point, known as the principal focus. In contrast, a concave lens is thinner in the middle and diverges light rays. The convex lens is also known as a converging lens, whereas a concave lens is a diverging lens.
2. Explain the key types of convex lenses and their specific uses in optical instruments.
Convex lenses are of three main types:
- Plano-convex lens: Curved outward on one side and flat on the other, often used for collimating light in devices like lasers, and in various optical sensors.
- Double convex (biconvex) lens: Curved outward on both sides, ideal for focusing light in projectors, cameras, microscopes, and telescopes.
- Concave-convex (meniscus) lens: One side concave, one side convex, used to correct spherical aberration and manage laser beams in optical systems.
3. State the lens formula for a convex lens and explain each term with its correct sign convention.
The lens formula is 1/f = 1/v + 1/u, where:
- f = focal length of the lens (positive for convex lens)
- v = image distance from the optical center (positive if the image is real and formed on the opposite side of the object)
- u = object distance from the optical center (always negative as per the sign convention when the object is placed to the left of the lens)
4. Describe with examples how a convex lens forms real and virtual images.
A convex lens forms real images when the object is placed beyond its focal point; these images are inverted and can be projected on a screen (e.g., images formed by a projector or camera). If the object is within the focal length, the lens forms a virtual image that is upright and cannot be captured on a screen, as in magnifying glasses.
5. List three important uses of convex lenses in everyday and scientific instruments.
- Used in magnifying glasses to enlarge small objects for easier viewing.
- Serve as primary components in microscopes and telescopes to gather and focus light for detailed observation.
- Employed in corrective spectacles for hypermetropia (farsightedness) to help focus images on the retina.
6. How does the magnification produced by a convex lens vary with the object's position?
Magnification (m) depends on the position of the object relative to the lens. It is given by m = height of image / height of object = v/u. As the object moves closer to the lens, magnification increases, making the image larger. If the object is within the focal length, the image appears virtual, upright, and magnified.
7. Compare the formation of images by a convex lens when the object is placed (i) at infinity, (ii) at the principal focus, and (iii) between the focal point and the optical center.
- At infinity: The image is formed at the principal focus, real, inverted, and highly diminished.
- At the principal focus (F): The image forms at infinity, is real and inverted, and cannot be captured on a screen.
- Between the focal point and the optical center: The image is virtual, enlarged, and upright, seen on the same side as the object.
8. Why is a double convex lens often preferred in optical instruments over a plano-convex lens?
A double convex lens has two symmetrically curved surfaces, which generally means it can achieve a shorter focal length and better convergence of light than a plano-convex lens of the same diameter. This property makes it preferable for high-precision instruments like microscopes and cameras, where sharper focusing is required.
9. How does changing the radii of curvature of a convex lens affect its focal length?
Reducing the radii of curvature (making surfaces more curved) decreases the focal length, bringing the focus closer to the lens. According to the lens maker’s formula, a smaller radius results in a stronger lens (lower focal length), while flatter surfaces (larger radii) increase the focal length.
10. What common misconception do students have about image formation by convex lenses, and how can it be corrected?
A frequent misconception is that a convex lens always produces a real image. In reality, it produces a virtual, upright, and magnified image when the object is placed within its focal length. To avoid this error, remember to analyze the position of the object relative to the focal point.
11. In what ways can convex lenses be used to concentrate solar energy, and what is the principle behind it?
Convex lenses can be used in solar concentrators to focus sunlight onto a small area, increasing the intensity of heat or light for applications like solar cells or burning glass demonstrations. The principle is based on the lens’s ability to converge parallel rays to its focal point.
12. If a 6 cm high object is placed 6 cm in front of an 18 cm focal length convex lens, what is the nature, position, and height of the image formed?
Using the lens formula: 1/v = 1/f - 1/u; f = +18 cm, u = -6 cm.
- 1/v = 1/18 + 1/6 = (1 + 3)/18 = 4/18 = 2/9
- v = 9/2 = 4.5 cm (positive, virtual, on the same side as object)
- Magnification: m = v/u = 4.5/(-6) = -0.75 (upright as image is virtual)
- Image height = m × object height = (-0.75) × 6 cm = -4.5 cm (upright, smaller)
