Image Formation From a Spherical Lens – Experiment Schools, Teachers, and Students
The laws of refraction govern the bending of light as it passes through a spherical lens. A spherical lens has two curved surfaces, and its ability to converge or diverge light is determined by the material’s refractive index and the curvature of the surfaces.
Theory
1. Laws of Refraction (Snell’s Law)
- The incident ray, the refracted ray, and the normal to the interface at the point of incidence all lie in the same plane.
- The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant:sin i / sin r = n
where:
- i: Angle of incidence
- r: Angle of refraction
- n: Refractive index of the medium
2. Rules for Ray Tracing
- A ray of light from the object, parallel to the principal axis, after refraction from a convex lens, passes through the principal focus on the other side of the lens. For a concave lens, the ray appears to diverge from the principal focus located on the same side of the lens.
- A ray of light passing through the principal focus, after refraction from a convex lens, will emerge parallel to the principal axis. A ray of light appearing to meet at the principal focus of a concave lens, after refraction, will emerge parallel to the principal axis.
- A ray of light passing through the optical center of a spherical lens continues in the same direction without deviation.
- A ray of light directed toward the center of curvature of a lens will pass through the lens along the same path, as it strikes the surface normally.
3. Lens Terminology
- Optical Center (O): The point within the lens through which light passes without deviation.
- Principal Axis: The straight line passing through the optical center and the centers of curvature of the lens.
- Focus (F): The point where parallel rays converge (convex lens) or appear to diverge (concave lens) after refraction.
- Focal Length (f): The distance between the optical center and the focus.
4. Lens Formula
The relationship between the object distance (u), image distance (v), and focal length (f) is given by:
1/f = 1/v – 1/u
5. Magnification (M)
The magnification of a lens is the ratio of the height of the image (hi) to the height of the object (ho):
M = hi / ho = v / u
6. Refraction at Spherical Surfaces
Light rays refract at each surface of the lens according to Snell’s law. The cumulative effect produces either convergence (convex lens) or divergence (concave lens) of light rays.
Applications of Spherical Lenses
1. Convex Lenses
- Used in magnifying glasses to produce enlarged images.
- Essential components of optical instruments like microscopes and telescopes.
- Employed in corrective lenses for hypermetropia (farsightedness).
2. Concave Lenses
- Used in eyeglasses to correct myopia (nearsightedness).
- Incorporated in laser systems for beam divergence.
- Found in cameras to control light paths.
Examples
- Converging Light: Parallel rays of light entering a convex lens converge at the focus after refraction.
- Diverging Light: Parallel rays of light entering a concave lens appear to diverge from a virtual focus.
- Magnifying Effect: An object placed within the focal length of a convex lens produces an enlarged, virtual, and upright image.
- Corrective Lenses: A concave lens placed in front of the eye of a myopic person diverges incoming light rays to focus them on the retina.
Real-Life Uses
- Designing corrective eyeglasses for vision impairments.
- Constructing optical instruments for scientific research and exploration.
- Producing photographic lenses with specific focusing properties.
- Focusing sunlight in solar energy systems.
Observations
- A convex lens converges light rays, forming real or virtual images depending on the object’s position.
- A concave lens always forms virtual, upright, and diminished images.
- Refraction follows Snell’s law at each surface of the lens, leading to image formation.
- The focal length of a lens depends on its curvature and the refractive index of its material.
