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Refraction by Spherical Lenses

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Last updated date: 24th May 2024
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Refraction of Light through Spherical Lenses

Refraction of light is defined as the process of changing the direction of light when it passes from one medium to another. The working of a lens is based on the concept of refraction of light when they pass through it. A lens is a piece of transparent glass that is bounded by two spherical surfaces and is used to magnify objects. They are of two types of lenses, they are the convex and concave lens. The image produced by the convex lens is magnified and the image produced by the concave lens is diminished.


The refractive index of glass is comparatively higher than that of the surrounding air. Light rays that pass from air to glass are refracted in general. By using a special type of spherical lens- convex lenses or concave lenses, the light rays passing through the lens either diverge or converge. The applications of lenses are widely used in various fields such as the construction of telescopes and microscopes, in cameras, and in projectors. Even our eyes are an example of a spherical lens.


What is a Spherical Lens?

When the curved face of a refracting element is of a spherical shape, these lenses are defined as Spherical lenses. Spherical lenses are of two types: Convex lenses and Concave lens. Convex lenses are types of lenses that have thick central portions and thin periphery. 


Concave lenses are types of lenses that have thin central portions and thick periphery. These lenses have a lot of uses across industries for their practical utility. From microscopes and telescopes to glasses and car mirrors, the general presence of these lenses or the fundamentals upon which they operate is virtually irreplaceable. 


Convex Lens

A convex lens is also called the converging lens because it converges the light rays that incident on it. The surface of the lens is convex in nature. If a light ray passes parallel to the principal axis of a convex lens, the ray is refracted through the focus. If the incident ray passes through the optical center, the ray does not get refracted. If the incident ray passes through the focus of the convex lens, the refracted ray is then said to pass parallel to the principal axis.


Concave Lens

A concave lens is also defined as a diverging lens as it diverges light rays that pass through it. The surface of the lens is concave in nature. An incident light ray parallel to the principal axis passes through a concave lens and gets diverged. When speculated, it appears to pass through the focus. If the incident light ray passes through the optic center, similar to the convex lens, the refracted ray does not get deviation. If the incident light ray passes through the focus, the ray gets refracted parallel to the principal axis.


Terms Commonly Associated with Lens

  1. Principal Axis: It is a straight line, hypothetically drawn, that links the center of curvature of the lens and optical center. It is always perpendicular to the vertical axis. We can calculate and locate the principal focus of the lens on the principal axis.

  2. Optical Centre: It is the center of the lens, which is determined geometrically. The optical center generally lies on the principal axis. When the light passes through the optical center, no deviation of light will take place.

  3. Centre Of Curvature: The lens is always a separate part of the sphere. So the actual center of the sphere, from which the lens is derived, is termed as the Centre of curvature. In other words, the space in between the point at which rays of the lens meet and the lens itself is denoted as the Centre of curvature.

  4. Principal Focus: We always consider incident rays as parallel to the principal axis. These rays, after striking the lens, either join or seem like joining at a certain point. That point at which the rays join or seem to join is known as Principal focus. It is also termed as the Focal point. The focus is present on both sides of the lens.

  5. Focal Length: It is the intermediate path or distance that lies between the optical center and principal focus. It is denoted by ‘f'. Commonly, the focal length of a concave lens will always be negative, and that of a convex lens will always be positive.


Lateral Magnification

When we calculate the ratio of the size of the image to the size of the object, the result we get is called Lateral magnification. It is also called linear magnification or transverse magnification. So, the mathematical expression of linear magnification is m=v/u. 


If the value of m is negative, the image will be inverted. If it is positive, the image will be upright.


Refraction Through Convex Spherical Lens

  1. When the Object is At Infinity:

The rays will move parallel to the principal axis, strike the lens, and then converge to meet at the focus. Thus, the image will be a real image at the focus. The size of the image will be a tiny or point image.

  1. When the Object is At Any Point Between the Double of Focus (2F) and Infinity:

One of the rays will move parallel to the principal axis, strike the lens, and then pass through the focus. The other ray will directly pass through the center of curvature to join the previous ray at any point between focus and double focus (2F). The characteristics of the images are- inverted, diminished, and real.

  1. When the Object is at Double of Focus or 2F:

One of the rays will move parallel to the principal axis, strike the lens, and then pass through the focus. The other ray after refraction through the spherical surface will pass through the center to join the previous ray at 2F. The image will be inverted but real. The image’s size and object’s size will be similar.

  1. When the Object is at any Point Between Focus and Double of Focus(2F):

One of the rays will move parallel to the principal axis, strike the lens, and then pass through the focus. The other ray after refraction at the spherical surface will pass through the center to join the previous ray at any point between 2F and infinity. The characteristics of the image are- inverted, magnified, and real.

  1. When the Object is Situated at Focus:

One of the rays will move parallel to the principal axis, strike the lens, and then pass through focus. The other ray will pass through the center. The two rays finally meet at infinity. The characteristics of the images are- inverted, real, and magnified to a large extent.

  1. When the Object is Situated at Focus:

Here, the image will be formed on the same side of the object. The image will be virtual. It will be straight and enlarged to a great extent.

  1. Refraction Through A Concave Spherical Lens:

When concave lenses are used, the images will be formed on the same side of the object. The image will be diminished, straight, and virtual. 


(Image to be Added Soon)


This is how spherical lenses refract light rays incident on them. Learn how different outcomes are witnessed due to the position of the source and lenses. Focus on how the light rays bend to understand the outcomes properly.

FAQs on Refraction by Spherical Lenses

1. What is the difference between the concavo-convex lens and the convexo-concave lens?

When we come across the refraction through spherical surface class 12, we encounter concavo-convex and convexo-concave lenses. The lens where the curvature is more towards the concave face in comparison to the convex face is termed as the Convexo-concave lens, whereas the lens where the curvature is more towards the convex face in comparison to the concave is termed as Concavo-convex lens. The concavo-convex lens behaves more likely as a convex lens, while the convexo-concave lens behaves more likely as a concave lens. They are both used as correcting lenses. 

2. What are the defects of images and how are they cured?

  • Spherical Aberration: It is cured by using a mirror that is parabolic in shape.

  • Astigmatism: It is usually corrected by using spectacles.

  • Myopia or Near-Sightedness: It is cured by using a concave lens.

  • Hypermetropia or Farsightedness: It is cured by using a convex lens.

3. What are the rules for obtaining images formed by the convex lens?

The image in a convex lens after refraction is formed at a point where the two refracted light rays meet.

  • Rule 1: An Incident ray parallel to the principal axis passes through the focus of the lens, after refraction.

  • Rule 2: An Incident ray that passes through the optical center of the convex lens after refraction goes straight and does not bend. Also, an incident ray of light passing along the path of the principal axis of a convex lens also goes straight and does not deviate after refraction.

  • Rule 3: An incident ray that passes through the focus of the convex lens after refraction becomes parallel to the principal axis.

4. What is the lens formula?

The lens formula is given by,

1/image distance  – 1/object distance = 1/ focal length 

or 1/v - 1/u = 1/f


Magnification produced by the lens:

Linear magnification is the size of the image relative to the object. Linear magnification can be measured by the ratio of the height of the image to the height of the object.

Magnification = height of image /height of object 

ot m = h2/h1

Another formula that is measured in terms of distance is

Magnification = image distance/object distance

5. What are the rules for obtaining images formed by a concave lens?

  • Rule 1: An Incident ray of light that is parallel to the principal axis of the concave lens after refraction appears to be passing from the focus of the lens.

  • Rule 2: An Incident ray of light that passes through the optical center of the concave lens after refraction goes straight.

  • Rule 3: An Incident ray of light passing through the focus on another side of the concave lens after refraction through the lens becomes parallel to the principal axis.

6. How to measure the power of a lens?

The following are the formulas used to measure the power of a lens,

  • The power of the lens is a measure of the degree to which a lens when subjected to light rays either converges or diverges.

  • Power of lens  = 1/ focal length of the lens (which is measured in meters)

  • P = 1/f

  • A lens that has a short focal length has more power in comparison to a lens with a long focal length. The SI unit of the power of the lens is dioptre.

7. What is a sign convention for spherical lenses?

According to the New Cartesian Sign Convention:

  • From the optical center of the lens, the distance can be measured.

  • The distance is measured in the same direction as that of the direction of the positive incident ray.

  • The distance which is measured opposite to the direction of the incident ray is considered negative.

  • The distance measured which is perpendicular and at the top of the principal axis is considered positive.

  • The distance measured perpendicular and downward to the principal axis is considered negative.

  • The object is generally located on the left-hand side of the lens.

  • The focal length of a convex lens is taken as positive.

  • The focal length of a concave lens is taken as negative.

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