Muskan Shafi Education Content Expert
Education Content Expert | Updated On - Mar 17, 2025
Lens is a part of a transparent thick glass bounded by two spherical surfaces. Spherical Lenses are optical instruments that cause light rays to converge or diverge depending on the type. Spherical lenses are divided into two types namely Concave Lens and Convex Lens.
- Concave Lenses are lenses that have two spherical surfaces bulging outwards.
- Convex Lenses are lenses that have two spherical surfaces bulging inwards.
- Magnification of Lens is the ratio of the height of the image to the height of the object.
Lens Formula is an equation that gives the relationship between the focal length, image distance, and object distance. Lens Formula is given as
\(\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\)
Here, v is the distance of the image from the lens, u is the distance of the object from the lens, and f is the focal length of the lens.
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| Table of Content |
Key Terms: Lens Formula, Spherical Lenses, Concave Lens, Convex Lens, Focal Length, Magnification, Power of a Lens, Light Rays
What are Spherical Lenses?
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Spherical Lens is a piece of transparent optical material with two spherical surfaces to refract light rays. They either converge or diverge light rays to form an image. Spherical Lenses can be classified into major types namely
- Concave Lens (Divergent Lenses)
- Convex Lens (Convergent Lenses)
Spherical Lenses
Concave Lens
- Concave lenses are formed by combining two spherical surfaces in such a manner that they are curved inwards.
- They are also called diverging lenses since they diverge the light rays falling on them.
- They are thicker at the edges and thinner in the middle.
Image Formation in Concave Lens
Convex Lens
- Convex lenses are formed by combining two spherical surfaces together in such a way that they are curved outwards.
- They are also called converging lenses as these lenses converge the light rays.
- They are thicker in the middle and thinner at the edges.
Image Formation in Convex Lens
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Lens Formula
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Lens Formula states the relationship between the distance of an object, the distance of an image, and the focal length of the lens in Optics. Lens formula is applicable to both concave and convex lenses. It is used to find image distance for both real images or virtual images.
Lens Formula is given as
| \( \frac{1}{v} + \frac{1}{u} = \frac{1}{f}\) |
Where
- v: Distance of the image from the lens.
- u: Distance of the object from the lens.
- f: Focal length of the lens.
Read More: Lens Maker's Formula
Solved ExampleExample: What is the distance of the image from the lens if the object is 6 cm away from a convex lens of focal length 3 cm? Solution: Given that
Using the Lens Formula, \( \frac{1}{v} + \frac{1}{u} = \frac{1}{f}\) 1/6 + 1/v = 1/3 1/v = 1/3 - 1/6 = 1/6 v = 6 cm Thus, the distance of the image from the lens is 6 cm. |
Sign Convention in Lens
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Lens formula can be used in all situations related to spherical mirrors with appropriate sign conventions. The images which are formed by the Concave and the Convex lens can be real or virtual as well as they may have different sizes.
- If the distance of the image is negative, then it is a virtual image on the same side of the lens as the object.
- If the formula has a negative (-ve) focal length, then the lens is a diverging lens.
Distance is always measured from the optical center of the lenses.
- If the image is virtual, then the distance of the image (v) is negative.
- If the image is real, the distance of the image (v) is positive.
The table given shows the sign conventions for spherical lenses:
| Distance | Positive Value (+) | Negative Value (-) |
|---|---|---|
| u | Real | Virtual |
| v | Real | Virtual |
| f | Convex Lens | Concave Lens |
Magnification
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Magnification of a lens is the ratio of the height of the image formed by the lens to the height of the object. Magnification is equal to the ratio of the image distance to that of the distance of the object. It is denoted by m. The formula of magnification using lens formula is:
Magnification Formula is given as:
| \( m = \frac{h’}{h} = \frac{v}{u} \) |
Where
- m: Magnification
- h': Height of the Image
- h: Height of the Object
Solved ExampleExample: What will be the height of the image if the object distance is 20 cm, the image distance is 60 cm, and the height of the object is 5 cm? Solution: Given that,
Using the Magnification Formula, \( m = \frac{h’}{h} = \frac{v}{u} \) h’ = 60/20 x 5 = 15 cm Thus, the height of the image is 15 cm. |
Power of a Lens
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Power of a Lens is the degree of convergence or divergence of the light rays falling on a lens. The degree of convergence or divergence of the light rays depends upon the focal length of the lens. The power of the concave lens is negative, whereas the power of the convex lens can be positive. Therefore, the power of a lens is the reciprocal of the focal length of the lens used.
Power of Lens is given by the formula:
| \(P = {1 \over f}\) |
Where
- f is the focal length of the lens measured in meter (m).
- P is the power with the SI unit Dioptre (D).
Solved ExampleExample: The power of a lens is given as +2.0D. Find the focal length of the lens and state the type of lens. Solution: The power of the lens is +2.0D. The power of a lens is given using the formula \(P = {1 \over f}\) +2.0 = 1/f f = 1/2 = +0.5 Thus, the focal length of the lens is 0.5 m or 50 cm. Since the focal length has a positive sign, it is a convex lens. |
Check More:
| Related Topics | ||
|---|---|---|
| Spherical Mirrors | Toric Lens | What is Fisheye Lens? |
| Power of Accommodation of the Eye | Concave and Convex Mirror | Mirror Formula Derivation |
Things to Remember
- Spherical Lenses are optical lenses with a curved surface causing the light rays to converge or diverge.
- Concave Lens and Convex Lens are the two types of spherical lenses.
- Lens Formula is used to describe the relationship between the focal length, image distance, and object distance.
- Lens Formula is given as \( \frac{1}{v} + \frac{1}{u} = \frac{1}{f}\).
- Magnification is defined as the ratio of the image distance to the distance of the object.
- Magnification of a lens is given as \( m = \frac{h’}{h} = \frac{v}{u} \).
- Power of a lens is a measure of the convergence or divergence of the light rays falling on a lens.
Sample Questions
Ques. What is a Lens? (1 Mark)
Ans. A Lens is a transparent material (glass) that has two surfaces, in which one of the surfaces or both surfaces are spherical. Lenses may be called magnifying glasses which have curved sides. Lenses are basically of two types which are Concave lenses and Convex lenses.
Ques. What is the image distance if the distance of an object of height 6 cm from a concave lens is 20 cm? The focal length is given as 10 cm. (3 Marks)
Ans. Since the given lens is Concave,
- Focal Length (f) = -10 cm
- Object distance (u) = + 20 cm
Using the Lens Formula,
\( \frac{1}{v} + \frac{1}{u} = \frac{1}{f}\)
1/v = 1/f - 1/u
1/v = - 1/10 - 1/20
1/v = - 3/20
Image Distance (v) = -20/3 = - 6.7 cm
Thus, the distance of the image is - 6.7 cm.
Ques. Differentiate between Concave and Convex Lenses. (5 Marks)
Ans. The difference between concave and convex lenses is as follows:
| Concave Lens | Convex Lens |
|---|---|
| Concave lenses are thinner in the middle and thicker at the edges. | Convex lenses are thicker in the middle and thinner at the edges. |
| They are also known as Diverging Lenses. | They are also known as Converging Lenses. |
| They are used in glasses, telescopes, spy holes in doors, etc. It is also used for the correction of the problem in short sight | They are used in cameras, overhead projectors, projector microscopes, simple telescopes, magnifying glasses, etc. |
| Concave lenses are used in the correction of short-sightedness. | Convex lenses are used in the correction of long-sightedness. |
| They have a negative focal length. | They have a positive focal length. |
Ques. What is Object Distance? (1 Mark)
Ans. Object Distance is the distance of the object which is measured from the optical center of the lens. The distance of an object from the optical center is called object distance. The object distance is denoted by u.
Ques. What will be the image distance if the distance of the object placed in front of a convex lens having a focal length of 10 cm is 15 cm? (3 Marks)
Ans. As the lens is Convex,
- Focal length (f) = 10 cm
- Object distance (u) = 15 cm
Using the Lens Formula,
\( \frac{1}{v} + \frac{1}{u} = \frac{1}{f}\)
1/v = 1/f - 1/o
1/v = 1/10 - 1/15
1/v = 1/30
Thus, image distance v = 30 cm.
Ques. What is Focal Length? (1 Mark)
Ans. The focal length can be defined as the distance of the Principal Focus from the optical center of a lens. Focal length is denoted by f and is measured in meters (m).
Ques. What is Magnification? (3 Marks)
Ans. Magnification is defined as the ratio of the height of the image height to the height of the object. In other words, it is the ratio of image distance to object distance. Magnification is denoted by the letter 'm'. The formula to find the magnification of a lens is given as follows:
\( m = \frac{h’}{h} = \frac{v}{u} \)
Here
- h' is the height of the image.
- h is the height of the object
- v is the distance of the image.
- u is the distance of the object.
A positive (+) sign of magnification indicates that the image is virtual and erect, whereas a negative (-) sign indicates that the image is real and inverted.
Ques. What is the use of Lens Formula? (1 Mark)
Ans. The lens formula is applicable in all situations related to spherical lenses with appropriate sign conventions. Thus, the lens formula is used to find the distance of an image whether it is a real or virtual image.
Ques. What is meant by the Power of a Lens? (3 Marks)
Ans. Power of a Lens is defined as the measure of the degree of divergence or convergence of a beam of light caused by a lens. The convergence and divergence of a lens are determined by the focal length of a lens. Thus, the power of a lens is reciprocal to its focal length.
\(P = {1 \over f}\)
The SI unit of Power of a Lens is Dioptre represented by the letter 'D'. A lens with a focal length of one meter has a power of one dioptre. Convex lenses have positive power, while concave lenses have negative power.
Ques. Which lens has a positive magnification? (1 Mark)
Ans. Both real and virtual images are formed by convex lenses, therefore the convex lens can produce either positive or negative. Real images always have negative Magnification whereas virtual images always have positive Magnification.
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