Convex Lens

A convex lens is a converging lens that brings incident light rays together at a point. These lenses are thicker at the center and thinner towards the edges. The images formed by a convex lens can be real or virtual. The power of a convex lens is positive, and it is commonly used to correct hypermetropia.

In this article, we will learn about the Convex Lens, exploring its properties, the formation of images, the characteristics of the images, the formula for calculating power, and magnification, along with its diverse applications.

What is a Convex Lens?

Convex lens, also known as converging lens. It is a lens that brings together parallel light beams. It has a distinctive shape, being thicker in the center and narrower at the top and bottom. Instead of curving inward, the edges curve outward. When light passes through the lens, it bends at a specific point depending on the angle at which it enters.

Definition of Convex lens

Convex lens is a transparent lens that is thicker at the center and thinner at the edges and causes parallel rays of light to converge as they pass through it.

Example of Convex Lens

Here are some of the common examples of the convex lens:

• Camera lens
• Eyeglasses to correct farsightedness
• Projector lens
• Magnifying glass
• Rifle scope
• Telescope lens
• Binoculars lens
• Microscope lens

Parts of Convex Lens

A convex lens, similar to other lenses, is composed of various components and characteristics that influence its optical properties. The following are the main parts of a convex lens:

Focal Length of Convex Lens:

• The focal length of a convex lens is defined as the distance from the center of the lens to the principal focus.
• In the case of a convex lens, the focal length is considered positive which signifies the convergence of light rays.

Optical Center:

• The optical center of a convex lens is a point on the principal axis where any ray of light passing through the center has not deviated.
• It is denoted by “O.”

Focus of Convex Lens:

• The focus of a convex lens is the particular point on the optical axis where parallel rays of light converge after passing through the lens.
• This focus is situated on the side opposite of the incident light.

Center of Curvature:

• The center of curvature of a convex lens coincides with the center of the sphere from which the lens is derived.
• For a convex lens, the center of curvature is on the same side as the curved surface.

Principal Axis:

• Principal Axis is an imaginary straight line that runs through the lens’s optical center and is perpendicular to the surfaces of a convex lens.

Types of Convex Lens

Convex lenses, also known as converging lenses, are used in various optical applications. They come in different shapes and forms, each with particular uses and characteristics. The main types of convex lenses include:

• Biconvex Lens
• Plano-Convex Lens
• Convexo-Concave Lens

Plano Convex Lens

• Lenses that are plano-convex are optical units that are capable of focusing the light to a particular point.
• It has one flat face and the other curves out.
• This type of lens is often used in not very precise things where the light is parallel, such as in robots, military equipment, and medicinal products.

Biconvex lens

• These lenses are curved outward on both sides and are commonly referred to as biconvex or convex lenses.
• Their focal lengths are shorter than the ones of Plano-convex lenses having the same surface radius and diameter.

Concave-convex lens

• This lens has a section that is curved out on one side and in on the other.
• It sharpens the off-focus images formed by other types of lenses and is widely used in the control of lasers.
• The concave-convex lens is also known as a meniscus lens.
• This lens is a union of both convex and concave lenses.

Properties of Convex Lens

Convex lenses, being converging lenses, possess several distinctive properties. Here are the key properties of convex lenses:

• Converging Nature: The primary property of a convex lens is its ability to converge or focus parallel rays of light. In contrast, parallel rays diverge due to diverging lenses, also known as concave lenses.
• Real Principal Focus: Convex lenses have a real principal focus. A real focal point is located on the opposite side of the lens from the incident light when parallel light rays flow through a convex lens.
• Positive Focal Length: A convex lens’s positive focal length indicates that it is converging. This positive value is crucial in lens formula calculations.
• Real Images: Images formed by convex lenses are real and can be projected onto a screen. These images are formed by the actual convergence of light rays.
• Inverted and Enlarged Images: Real images formed by convex lenses are inverted and enlarged compared to the object. The object’s position concerning the focus point determines the degree of enlargement.
• Focal Point and Focal Length Relationship: A convex lens’s focal point is situated on the other side of the incident light. The focal length, which is positive, is calculated by measuring the distance between the lens’s optical center and its actual focus point.

Sign Convention of a Convex Lens

The sign convention for a convex lens is as follows:

Focal Length (f):

• The focal length for a convex lens is positive. This occurs because a convex lens converges light, and the focal point is located on the opposite side of the lens from the incident light.

Object Distance (u):

• Object Distance is measured from a particular object to the lens. When the object is positioned on the same side as the incident light (the side from which light approaches the lens), it is considered negative.

Image Distance (v):

• The image distance refers to the distance from the lens to the image. For images formed on the opposite side of the lens from the incident light, the distance is considered positive (real image).

Height (h):

• When measuring heights, positive values are assigned to upward measurements, while negative values are assigned to downward measurements.

Table of Sign Convention for Convex Lens

Following Table summarizes sign convention of Convex Lens:

Parameter	Sign
Focal Length (f)	Positive
Object Distance (u)	Negative (opposite the direction of incident light)
Image Distance (v)	Positive (in the direction of the incident light), Negative(opposite the direction of incident light)
Object Height (h)	Positive (upward)

Convex Lens Ray Diagram

A ray diagram is a graphical respresentation to make you understand about how images are formed by lenses. Now, we will create a ray diagram for a convex lens.

Image Formation by Convex Lens

Object at Infinity:

• Image is formed at the focal point (F) on the opposite side of the lens.
• Real, inverted, and highly diminished.

Object at Beyond 2F:

• Image is formed between F and 2F on the opposite side of the lens.
• Real, inverted, and diminished.

Object at 2F:

• Image is formed at 2F on the opposite side of the lens.
• Real, inverted, and the same size as the object.

Object in Between F and 2F:

• Image is formed beyond 2F on the opposite side of the lens.
• Real, inverted, and enlarged.

Object at F:

• Image is formed at infinity on the opposite side of the lens.
• No real image is formed, only a virtual image.

Object Distance Less than F:

• Image is formed on the same side as the object.
• Virtual, upright, and enlarged.

Table for Image formation in Convex lens

All the possible cases of image formation can be see

Object Position	Image Position	Image Size	Image Nature
Beyond 2F	Between F and 2F	Smaller	Real, Inverted
At 2F	At 2F	Same Size	Real, Inverted
Between F and 2F	Beyond 2F	Larger	Real, Inverted
At F	Infinity	Infinite	Real, Inverted (Highly Diminished)
Between F and Lens	Beyond 2F	Larger	Virtual, Upright
At Lens	At Lens	Magnified	Virtual, Upright
Object Inside Lens	Between Lens and F	Larger	Virtual, Upright

Real and Virtual Image in Convex lens

A convex lens is capable of forming both real and virtual images.

• An object forms a virtual and upright picture when it is positioned between the focus and the optical center
• Real and inverted image when it is positioned beyond the focal point.

Formula of Convex Lens

The lens formula is an equation that explains how the object distance (u), image distance (v), and focal length (f) of a lens are related. This formula works for both convex and concave lenses. In the case of a convex lens, the focal length is considered positive. The lens formula for a convex lens is:

(1/f) = (1/v)-(1/u)

Where:

• f represents the focal length of the lens.
• v represents the image distance (distance from the lens to the image formed).
• u represents the object distance (distance from the lens to the object).

Magnification Formula of Convex Lens

For a convex lens, the magnification formula is the same as for a concave lens, except that the magnification for a convex lens is usually positive. This is because a convex lens converges light, creating a real, inverted image on the other side of the lens.

The magnification is denoted by “m”, is given by the formula:

m = h_image/h_object

Where:

• m represents the magnification.
• h_image represents the height of the image formed by the lens.
• h_object represents the height of the object.

In terms of object distance (u) and image distance (v), the magnification formula for a convex lens is:

m = v/u

Where:

• m represents the magnification.
• u represents the object distance (distance from the object to the lens).
• v represents the image distance (distance from the image to the lens).

The presence of a positive sign in the equation indicates that the image is formed on the opposite side of the object for a converging lens, like a convex lens.

Power of Convex Lens

The power of a convex lens is its ability to converge incident rays of light. The formula for the power of a convex lens is given by:

P = 1/f

where,

• P is Power
• f is focal length of the lens in m

Convex lenses possess positive focal lengths, which consequently results in the convex lens having a positive power.

Difference between Concave and Convex Lens

The difference between concave and convex lens is tabulated below:

Property	Convex Lens	Concave Lens
Nature of Lens	Converging lens	Diverging lens
Principal Focus	Real	Virtual
Focal Length	Positive	Negative
Shape	Thicker at the center, thinner at the edges	Thinner at the center, thicker at the edges
Examples	Camera, Human eye	Lights, Flashlights

Applications of Convex Lens

Some common applications of convex lenses are as follows:

• Camera Lenses: The present technology involves using convex lenses in cameras to brighten light onto the image sensor or film.
• Eyeglasses and Contact Lenses: Convex lenses can be found in eyeglasses and contact lenses that treat hypermetropia (farsightedness).
• Magnifying Glasses: Convex lenses are used in magnifying glasses to increase the size of the viewed objects.
• Microscopes: Convex lenses are used in microscopes to enlarge the image, making it possible for it to be seen through the eye.
• Telescopes: Astronomers use convex lenses in telescopes so that they can see celestial bodies more clearly.

Convex Lens is used to Correct Hypermetropia

In case of hypermetropia, the converging power of eye lens decreases, hence, the image is formed beyond retina. In this case, convex lens is used to increase converging power of eye. This led to the image formation on retina and thus correcting hypermetropia.

Convex Lens Solved Examples

Example 1: An object placed from a lens produces a virtual image at a distance of 5 cm in front of the lens. Calculate the focal length of the lens.

Solution:

Given:

• u = – 5
• v = – 25

Using the lens formula:

1/v – 1/u = 1/f

Substitute the known values:

(1/- 5) – (1/- 25) = (1/f)

Solve for f:

1/f = – 5+1/25

1/f = – 4/25

f = 0.16 cm

So, the focal length of the lens is 0.16 cm.

Example 2: What is the focal length of a convex lens, when a convex lens of focal length 30 cm in contact with a concave lens of focal length 20 cm?

Solution:

Given:

Focal length of the convex lens = 30 cm

Focal length of the concave lens = – 20 cm

Using the formula for the combination of lenses:

1/f = 1/f₁ + 1/f₂

1/f = (1/30) – (1/20) = -1/60

Therefore, combined focal length f = -60

Example 3: An object is places at a distance 40 cm from a thin converging lens of focal length; 10cm. Calculate the image distance.

Solution:

Given that

• f = 10 cm
• u = -40 cm

Using the lens formula:

1/v – 1/u = 1/f

Substitute the known values:

(1/v) – (1/ – 40) = 1/10

Solve for v:

1/v = (1/10) + (1/ – 40)

1/v = 3/40

Therefore, v = 40/3

So, the image distance is 40/3 cm

Convex Lens Practice Questions

Q1. What is the position of image when an object is placed at a distance of 10 cm from a convex lens of focal length 10 cm?

Q2. A convex lens of focal length 0.10 m is used to form a magnified image of an object of height 5 mm placed at a distance of 0.08 m from the lens. Find the position, nature, and size of the image.

Q3. A convex lens produces an inverted image magnified three times of an object at a distance of 15 cm from it. Calculate the focal length of the lens.

Q4. A small object is so placed in front of a convex lens of 5 cm focal length that a virtual image is formed at a distance of 25 cm. Find the magnification.

Convex Lens Frequently Asked Questions

What are the different types of convex lenses?

The main types of convex lenses include Biconvex Lens, Plano-Convex Lens, and Convexo-Concave Lens.

What is the power of a convex lens?

The power of a convex lens is also positive.

What is the focal length of a convex lens?

Focal length of convex lens is the distance between the optical center and focus of convex lens

What type of image is formed by a convex lens?

The image formed by convex lens can be both real and virtual depending upon position of object

Is a convex lens diverging or converging?

Convex lenses are converging.