Concave Lens

Concave Lens is a diverging lens that scatters the incident light after refraction. Concave Lens is thinner in the middle and thicker at the edges. The images formed by a concave lens are virtual and erect. Power of the Concave lens is negative and it is widely used in the correction of myopia.

In this article, we will learn in detail about the Concave Lens, its properties, image formation, characteristics of the image, formula for calculating power, and magnification along with its application.

What is Concave Lens?

Concave Lens, also known as a diverging lens, is a type of lens that is thinner at the center than at the edges. It is characterized by its inward-curved surfaces. Unlike a convex lens, which converges light rays, a concave lens causes parallel rays of light to diverge, or spread out.

Concave Lens Definition

A concave lens is a lens that is thinner at the center than at the edges, causing parallel rays of light to diverge as they pass through it.

Example of Concave Lens

Following are the some common examples of the concave lens:

• Binoculars and telescopes.
• Eye Glasses to correct nearsightedness.
• Cameras.
• Flashlights.
• Lasers (CD, DVD players for example).

Parts of Concave Lens

A concave lens, like other lenses, consists of several parts and features that contribute to its optical properties. Here are the main parts of a concave lens:

Focal Length of Concave lens

• Focal length Lens is the distance between the center of the lens and the principal focus.
• For a concave lens, the focal length is considered negative, indicating divergence of light.

Optical Center

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

Focus of Concave Lens

• The focus is the point on the optical axis where parallel rays of light appear to diverge from (for a concave lens) after passing through the lens.
• The focus is on the same side as the incident light.

Center of Curvature

• Center of curvature is the center of the sphere from which the lens is been created.
• For a concave lens, the center of curvature is on the side opposite the curved surface.

Principle Axis

• The principal axis is an imaginary straight line that passes through the optical center of a lens, perpendicular to the lens surfaces.

Types of Concave lens

Concave lenses, also known as diverging lenses, come in various shapes and forms depending on their specific applications and designs. The main types of concave lenses include:

• Biconcave Lens
• Plano-Concave Lens
• Convexo Conacve Lens

Types of Concave Lens

Biconcave Lens

• Biconcave Lens is characterized by two curved surfaces, both of which are concave.
• It is symmetrical, with the curves facing each other.
• This lens is thinner at the center than at the edges, and it diverges parallel rays of light.

Plano Concave Lens

• Planoconcave lens is a type of lens with one flat (plano) surface and one concave surface.
• The flat side is typically facing away from the center of the lens.
• It is a diverging lens, meaning it causes parallel rays of light to spread out.

Convexo-Concave Lens

• Convexo-concave lens has two different surfaces one as convex surface and other as concave surface.
• The convex side is typically facing outward.
• This lens type can be thought of as a combination of a convex lens and a concave lens, and its optical properties are determined by the radii of curvature of its surfaces.

Double Concave Lens

• “Double Concave Lens” is interchangeable with the biconcave lens.
• It refers to a concave lens with two curved surfaces that are both concave.
• This lens type is frequently used for its diverging properties and is thinner in the middle than at the edges.

Properties of Concave Lens

Concave lenses, being diverging lenses, possess several distinctive properties. Here are the key properties of concave lenses:

• Diverging Nature: The primary property of a concave lens is its ability to diverge or spread out parallel rays of light. This is in contrast to converging lenses (convex lenses) that focus parallel rays to a point.
• Virtual Principal Focus: Concave lenses have a virtual principal focus. When parallel rays of light pass through a concave lens, they appear to diverge from a virtual point on the same side as the incident light. The focal point is considered virtual for a concave lens.
• Negative Focal Length: The focal length of a concave lens is negative. This indicates the diverging nature of the lens and is a crucial parameter in lens formula calculations.
• Virtual Images: Images formed by concave lenses are virtual. They cannot be projected onto a screen and are perceived by the observer as if the light is coming from a virtual source.
• Upright and Diminished Images: Virtual images formed by a concave lens are upright and diminished in size compared to the object. The extent of diminishment depends on the position of the object relative to the focal point.
• Focal Point and Focal Length Relationship: The focal point of a concave lens is located on the same side as the incident light. The focal length is measured from the optical center of the lens to this virtual focal point and is considered negative.

Sign Convention of Concave Lens

Following are the Sign Conventions for the Concave lens:

1. Focal Length(f)
   • The Focal length for the Concave lens is Negative. This is because a concave lens diverges light, and the focal point is on the same side as the incident light.
2. Object Distance(u)
   • Object distance is measured from the object to the lens. If the object is on the same side as the incident light (the side from which light approaches the lens), it is taken as negative.
3. Image Distance(v)
   • Image distance is the distance between the image to the lens. For images formed on the same side as the incident light, the distance is considered negative (virtual image).
4. Height(h)
   • Heights measured upwards are considered positive, and heights measured downwards are considered negative.

Table of Sign Convention for Concave lens

Following Table summarizes sign convention of Concave Lens:

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

Ray Diagram of Concave Lens

Ray Diagram is a graphical representation used to understand the image formation by lenses. Let’s draw a ray diagram for a concave lens:

Ray diagram for Object at Infinity:

• If the object is at an infinite distance from the concave lens (essentially parallel rays), the diverging rays continue to spread out after passing through the lens.
• The extended rays appear to diverge from a virtual focal point on the same side as the object.
• The image formed is virtual, upright, and diminished.

Concave Lens – Ray Diagram for Object at Infinity

Ray Diagram for Object between Infinity and Optical Centre:

• The diverging rays, when extended backward, appear to diverge from a point on the same side as the object.
• The correct description is that the image formed is virtual, erect, and diminished (smaller than the actual object).

Concave Lens – Object between Infinity and Optical Center

Table for Image formation in Concave lens

Object position	Image Position	Image nature	Image size
At infinity	At F1	Virtual and Erect	Highly diminished, point-sized
Between Infinity and Optical Centre	Between Focus (F1) and Optical center (O)	Virtual and Erect	Diminished

Concave Lens Formula

The lens formula is a mathematical relationship that describes the relationship between the object distance (u), the image distance (v), and the focal length (f) of a lens. The formula is applicable to both convex and concave lenses. For the concave lens , focal length is considered as negative.

The lens formula is given by:

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

Where:

• f represents 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).

Concave Lens Magnification Formula

The magnification formula relates the height of an image to the height of an object in optics.

For a lens, including a concave lens, the magnification (often denoted as “m“) is given by the following 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 the context of concave lenses, it’s important to note that the magnification for such lenses is generally negative. This negative sign indicates that the image formed is virtual, upright, and on the same side as the object. Since concave lenses diverge light, the virtual image is produced by extending backward the divergent rays that appear to converge.

The magnification formula can also be expressed in terms of object distance (u) and image distance (v) for both convex and concave lenses.

The formula is as follows:

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 negative sign in the formula indicates that the image is formed on the same side as the object for a diverging lens, such as a concave lens.

Learn, Lens Formula and Magnification

Power of Concave Lens

Power of Concave Lens is the ability of concave lens to diverge the incident rays. The formula for Power of concave lens is given by

P = 1/(-f)

where,

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

Since, focal length of concave lens is negative therefore minus sign is placed before ‘f’ in the formula. This implies that Power of Concave Lens is negative

Concave and Convex Lens

Below is the difference between the Concave and Convex lens:

Feature	Concave Lens	Convex Lens
Shape	Thinner at the center, curved inward	Thicker at the center, curved outward
Nature of Lens	Diverging lens	Converging lens
Principal Focus	Virtual, on the same side as the incident light	Real, on the opposite side from the incident light
Focal Length	Negative	Positive
Effect on Parallel Rays	Rays diverge after passing through	Rays converge after passing through
Image Formation	Virtual, upright, and diminished	May be Real or virtual, inverted or upright, and magnified or diminished
Common Applications	Corrective eyeglasses for myopia, projectors, optical instruments with diverging needs	Corrective eyeglasses for hyperopia, cameras, magnifying glasses, optical instruments requiring convergence

Learn, Difference Between Concave and Convex Lens

Applications of Concave Lens

Concave lenses, also known as diverging lenses, have various applications in optics and technology. Their ability to diverge parallel rays of light is utilized in different contexts. Here are some common applications of concave lenses:

1. Corrective Eyewear:
   • Concave lenses are used in eyeglasses to correct vision problems such as nearsightedness (myopia). By causing parallel rays of light to diverge before entering the eye, a concave lens helps bring the image into focus on the retina.
2. Projectors:
   • Concave lenses are used in projectors to spread out light rays. This is especially useful for creating a wider and larger image projection on a screen.
3. Camera Systems:
   • Certain optical systems, including cameras, use concave lenses to diverge light rays. In some camera designs, concave lenses are used to correct aberrations and distortions.
4. Flashlights and Car Headlights:
   • Some flashlights and car headlights use concave lenses to spread out light, providing a wider and more even illumination.
5. Binoculars and Spotting Scopes:
   • In optical instruments like binoculars and spotting scopes, concave lenses may be used in combination with convex lenses to enhance the overall performance of the system.
6. Galilean Telescopes:
   • Galilean telescopes use a convex objective lens and a concave eyepiece. The concave eyepiece helps increase the eye relief and provides a wider field of view.

Concave Lens – Solved Examples

Example 1: An object is placed 20 cm in front of a concave lens with a focal length of -15 cm. Determine the image distance and describe the characteristics of the image formed.

Solution:

Given

• Object distance (u) = -20 cm (negative since the object is in front of the lens)
• Focal length (f) = -15 cm (negative for a concave lens)

Using the lens formula:

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

Substitute the known values:

(1/-15) = (1/v) – (1/-20)

Solve for v:

1/v = (1/-15) – (1/20)

1/v = -(7/60)

v = -8.57 cm

The image distance (v) is 8.57 cm. The negative sign indicates that the image is formed on the same side as the incident light. The image which we get will be virtual, upright, and diminished.

Example 2: A concave lens has a focal length (f) of -10 cm. An object is placed 20 cm in front of the lens. Determine the image distance (v).

Solution:

Given:

u = -20 cm

f = -15 cm

Using the lens formula:

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

Substitute the known values:

(1/-10) = (1/v)-(1/-20)

Solve for v:

1/v = (1/-10)-(1/-20)

1/v = -(2/20)

v = -10 cm

So, the image distance (v) is -10 cm.

Example 3: A concave lens with a focal length (f) of -12 cm is used to form an image. An object is placed 24 cm in front of the lens. Determine the image distance (v). Calculate the height of the image formed if the object has a height of 6 cm.

1. Determine the image distance (v).
2. Calculate the height of the image formed if the object has a height of 6 cm.

Solution:

1. Calculation of Image Distance (v):

u = -24 cm

f = -12 cm

Using the lens formula:

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

Substitute the known values:

(1/-12)= (1/v) -(1/-24)

Solve for v:

1/v = (1/-12)-(1/24)

1/v = -(3/24)

v = -8 cm

So, the image distance (v) is -8 cm.

2. Calculation of Image Height:

Given:

h_object = 6 cm

The magnification (m) is given by the formula:

m = v/u

Substitute the values:

m = (−8/−12)

The image height (h_image) is related to the object height by the magnification:

h_image = m × h_object

Substitute the values:

h_image = (8/12) × 6 = 4 cm

So, the height of the image is 4 cm.

Example 4: Suppose you have a concave lens with an object placed 20 cm in front of it, and the image is formed at 10 cm. Find the focal length.

Solution:

Given:

u = -20 cm

v = -10 cm

Using the lens formula:

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

Substitute the known values:

(1/f) = (1/-10)-(1/-20)

Solve for f:

f = 1/((1/-10)-(1/-20)

f = 1/(-2/20)

f = 20/-2 cm

f = -10

So, the focal length is 10 cm.

Concave Lens – Practice Questions

Q1. A concave lens forms a virtual image when an object is placed 15 cm in front of it. If the image distance is -30 cm, find the focal length.

Q2. For a concave lens, an object is placed 25 cm in front of it, and the resulting image is formed at -50 cm. Determine the focal length.

Q3. A concave lens is used to form an image. If the object distance is -18 cm and the image distance is -9 cm, calculate the focal length.

Q4. Suppose a concave lens forms a virtual image when the object is placed 12 cm in front of it, and the image distance is -24 cm. Determine the focal length.

Q5. For a concave lens, the object distance is -30 cm, and the image is formed at -15 cm. Find the focal length.

Concave Lens Frequently Asked Questions

What is Concave Lens?

Concave lens is characterized by its inward-curved shape and is also known as a diverging lens because it causes parallel rays of light to diverge.

What are the Applications of Concave Lenses?

Concave lenses have various applications, including corrective eyewear for myopia, projectors, camera systems, flashlights, binoculars, telescopes, collimators, and more.

What are different types of Concave Lens?

The main types of concave lenses include double concave lenses (biconcave lenses), plano concave lenses, and convexo-concave lenses.

What is the Nature of Image Formed by Concave Lens?

A concave lens forms virtual images that are upright and either magnified or diminished, depending on the object’s position relative to the focal point of the lens.

What is the Lens formula for a Concave Lens?

The lens formula for a concave lens is (1/f)= (1/v)-(1/u) where f is the focal length, v is the image distance, and u is the object distance.

Why are Concave Lenses used in Eyeglasses for Myopia?

Concave lenses are used in eyeglasses for myopia (nearsightedness) to diverge incoming light before it reaches the eye, allowing the image to focus properly on the retina.

What happens if an Object is Placed at the Focal Point of a Concave Lens?

If an object is placed at the focal point of a concave lens, the rays of light become parallel after passing through the lens, and no well-defined image is formed.

What is difference between Concave and Convex Lens?

The main difference between Concave Lens and Convex Lens is that Concave lens is diverging and convex lens is converging. For detail, refer to the article