Refraction of Light through Curved Surfaces
Introduction
In our previous lessons, we learned about the basic concepts of refraction of light when it passes through a plane surface. In this lesson, we will explore the refraction of light when it passes through curved surfaces such as lenses.
Convex Lens
A convex lens is thicker at the center than at the edges. When light passes through a convex lens, it converges to a point known as the focal point. This phenomenon is called converging refraction.
Example 1: Object at Infinity
If the object is placed at an infinite distance from the convex lens (parallel to the principal axis), the rays after refraction will converge to a point on the principal axis. The image formed will be real, highly diminished, and formed at the focus of the lens.
Example 2: Object Behind 2F
If the object is placed beyond 2F (but not at infinity), the rays after refraction will converge to a point on the principal axis. The image formed will be real, smaller than the object, and located between F and 2F on the opposite side of the object.
Example 3: Object on 2F
If the object is placed exactly at 2F, the rays after refraction will converge and pass through 2F on the opposite side of the lens. The image formed will be real, of the same size as the object, and located at 2F on the opposite side of the lens.
Example 4: Object Between 2F and F
If the object is placed between 2F and F, the rays after refraction will converge and pass through 2F on the same side as the object. The image formed will be real, enlarged, and located beyond 2F on the opposite side of the object.
Example 5: Object on F
If the object is placed exactly at the focus (F), the rays after refraction will become parallel to the principal axis. The image formed will be formed at infinity and cannot be obtained on the screen.
Example 6: Object Between F and Optical Center
If the object is placed between F and the optical center, the rays after refraction will diverge. The image formed will be virtual, erect, and larger than the object. The image will be formed on the same side as the object.
Sign Convention
For the refraction of light through lenses, we use a sign convention to denote the direction of light rays. The convention is as follows:
- Distances measured in the direction of incident light are taken as positive.
- Distances measured in the opposite direction of incident light are taken as negative.
- Focal length of a convex lens is considered as positive.
- Focal length of a concave lens is considered as negative.
Applications
The refraction of light through curved surfaces has various practical applications in our daily lives. Some common applications include:
- Camera lenses: Convex lenses are used to converge light and form images in cameras.
- Glasses: Eyeglasses use lenses to correct vision problems.
- Microscopes: Microscopes use lenses to magnify small objects.
- Telescopes: Telescopes use lenses to gather and focus light from distant objects.
Concave Lens
A concave lens is thinner at the center than at the edges. When light passes through a concave lens, it diverges. This phenomenon is called diverging refraction.
Example 7: Object at Infinity
If the object is placed at an infinite distance from the concave lens (parallel to the principal axis), the rays after refraction will appear to diverge from a point on the principal axis. The image formed will be virtual, upright, and located at the focus of the lens.
Example 8: Object Behind the Lens
If the object is placed in front of the concave lens but at a distance greater than the focal length, the rays after refraction will still diverge. The image formed will be virtual, upright, and located between the lens and its focus on the same side as the object.
Example 9: Object at the Focus
If the object is placed exactly at the focal point (F), the rays after refraction will emerge parallel to the principal axis. The image formed will be formed at infinity and cannot be obtained on the screen.
Example 10: Object Between the Lens and the Focus
If the object is placed between the lens and the focus (but not at the focus), the rays after refraction will still diverge. The image formed will be virtual, upright, and located beyond the focal point on the same side as the object.
Example 11: Object at the Optical Center
If the object is placed exactly at the optical center, the rays after refraction will continue in the same direction. The image formed will be of the same size as the object and located at the optical center on the same side as the object.
Example 12: Object Between the Optical Center and the Lens
If the object is placed between the optical center and the lens, the rays after refraction will still diverge. The image formed will be virtual, upright, and larger than the object. The image will be formed on the opposite side of the object.
Applications
The refraction of light through curved surfaces, both convex and concave lenses, has various practical applications in our daily lives. Some common applications of concave lenses include:
- Correction of Nearsightedness: Concave lenses are used in eyeglasses to correct nearsightedness (myopia) by diverging light rays before they reach the eye's lens, helping focus distant objects on the retina.
- Galilean Telescope: A Galilean telescope uses a concave objective lens and a convex eyepiece lens to magnify distant objects. The concave lens produces a virtual and diminished image, which is further magnified by the convex eyepiece lens.
- Binoculars: Binoculars use multiple lenses, including concave lenses, to produce a wider field of view and provide a clearer image.
- Projectors: Concave lenses are used in slide projectors to diverge light and enlarge the image projected onto a screen.
- Viewfinders: Some cameras use concave lenses in their viewfinders to help photographers frame their shots and focus.
Conclusion
Understanding the refraction of light through curved surfaces, including both convex and concave lenses, is crucial in various optical applications. These lenses exhibit different behaviors, and they have significant practical uses in our daily lives, from correcting vision problems to enabling advanced imaging and magnification technologies.