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
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.
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.
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.
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.
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
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.
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.
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.
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.
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.
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.
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 meant by refraction through spherical lenses, and how does it differ from refraction in plane surfaces?
Refraction through spherical lenses refers to the bending of light rays as they pass through lenses with spherical surfaces, such as convex or concave lenses. Unlike refraction in plane surfaces, spherical lenses cause light to either converge or diverge due to their curved nature, resulting in image formation at specific points. This property is used in devices like microscopes, cameras, and the human eye.
2. What are the key differences between convex and concave lenses with respect to image formation?
- Convex lenses converge parallel rays to a focus and can form real, inverted, magnified, or diminished images depending on object position.
- Concave lenses diverge parallel rays and always produce virtual, upright, and diminished images.
- Convex lenses have a positive focal length; concave lenses have a negative focal length.
3. What is the lens formula and how is it applied in solving numerical problems for board exams?
The lens formula is 1/v - 1/u = 1/f, where 'v' is image distance, 'u' is object distance, and 'f' is the focal length. This equation is crucial in CBSE 2025–26 board exams for solving image position, focal length, or object distance problems related to spherical lenses. Make sure to follow sign conventions as per the New Cartesian method while applying this formula.
4. What are the main sign conventions for spherical lenses important for CBSE exams?
The New Cartesian Sign Convention for spherical lenses states:
- Object distances (u) are negative if measured against the incident light direction.
- Image distances (v) are positive if on the direction of light travel.
- Focal length (f) is positive for convex lenses, negative for concave lenses.
- Heights measured upwards from the principal axis are positive; downwards are negative.
5. How do you differentiate between a concavo-convex and a convexo-concave lens in terms of usage?
A concavo-convex lens has more curvature on the convex side and functions similarly to a convex lens, used to converge light. Conversely, a convexo-concave lens has greater curvature on the concave side and acts like a concave lens, used to diverge light. Both are used in corrective optics for vision defects.
6. In what situations does a convex lens form a magnified image, and why is this important in real-world applications?
A convex lens forms a magnified, real image when the object is placed between the focal point (F) and twice the focal length (2F). When the object is at F, the image is magnified and formed at infinity. This principle is essential in designing microscopes, magnifying glasses, and optical instruments to achieve enlargement of small objects.
7. What is lateral magnification in spherical lenses and how is it calculated for exam questions?
Lateral magnification (m) is the ratio of the height of the image (h2) to the height of the object (h1), given by m = v/u or m = h2/h1. For convex lenses, m can be greater or less than 1 depending on image size; for concave, it is always less than 1 as the image is diminished.
8. What common conceptual mistakes should students avoid when solving numerical problems on refraction by spherical lenses?
Students should avoid:
- Confusing sign conventions for u, v, and f.
- Mixing up real and virtual image criteria for convex vs. concave lenses.
- Forgetting that power (P) of a lens is P = 1/f, with f in meters and sign following the lens type.
- Incorrectly identifying the principal focus and principal axis in ray diagrams.
9. How are spherical aberration and astigmatism related to spherical lenses, and how are they corrected?
Spherical aberration occurs when light rays passing through a lens fail to meet at a single point, causing a blurred image. It is reduced using parabolic mirrors or combining lenses. Astigmatism is corrected using specially shaped lenses (cylindrical lenses) in spectacles to ensure sharp focus on the retina.
10. Why is understanding the concept of principal axis and optical centre essential in board theory and ray diagram questions?
The principal axis provides a reference line for constructing ray diagrams and applying sign conventions. The optical centre ensures rays passing through it do not deviate, simplifying image location. Accurate identification is vital for solving questions involving image formation, especially in CBSE theory and HOTS questions.
11. How do applications of spherical lenses demonstrate their importance in everyday life?
- Convex lenses are used in magnifiers, cameras, corrective glasses for hypermetropia, and optical instruments.
- Concave lenses are used in peepholes, lasers, and correcting myopia.
- Understanding these applications helps relate physics concepts to daily scenarios and real-world utility.
12. What would happen if the lens power is zero and how is this used in practical devices?
If the power of a lens is zero, its focal length is infinite, meaning it does not converge or diverge light rays. Such lenses are used in devices where no change in the light path is desired, or as reference standards in optics experiments.
