25.6 Image Formation by Lenses
3 min read•june 18, 2024
Lenses are optical devices that bend light to form images. They're crucial in many everyday tools, from eyeglasses to cameras. Understanding how lenses work helps us grasp the principles of optics and image formation.
Ray tracing is a key technique for predicting image characteristics with lenses. By following specific rules and tracing key light rays, we can determine an image's position, size, and orientation. This method reveals how object distance affects image formation.
Image Formation by Lenses
Rules for thin lens ray tracing
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- Ray tracing determines position, size, and orientation of image formed by
- Thin lens has thickness negligible compared to diameter
- Three key rays used in ray tracing:
- refracts through lens and passes through on other side
- passes through center of lens and continues straight without changing direction
- passes through on object side and refracts parallel to on other side
- Image forms at point where three key rays intersect after passing through lens
Image formation through ray tracing
- To find image formed by thin lens using ray tracing:
- Draw optical axis, lens, and object
- Draw three key rays from top of object:
- Parallel ray drawn parallel to optical axis from top of object, then through lens and focal point on image side
- Central ray drawn from top of object through center of lens, continuing straight
- Focal ray drawn from top of object through focal point on object side, then refracted parallel to optical axis on image side
- Point where three rays intersect on image side is top of image
- Draw line from this point perpendicular to optical axis to determine image's position and size
- Image characteristics depend on object's distance from lens:
- Object beyond 2F (twice focal length) produces real, inverted, smaller image
- Object between F and 2F produces real, inverted, larger image
- Object at 2F produces real, inverted, same size image
- Object between lens and F produces virtual, upright, larger image
- of the image is determined by the ratio of image size to object size
Lens power from focal length
- Lens (P) is reciprocal of focal length (f) in meters
- Unit of power is (D), reciprocal of meter (m⁻¹)
- Shorter focal length has higher power and stronger converging or diverging effect (magnifying glass)
- Longer focal length has lower power and weaker converging or diverging effect (telescope)
- Converging (positive) lenses have positive power
- Converging lens with 0.25 m focal length has power of D
- Diverging (negative) lenses have negative power
- with -0.5 m focal length has power of D
Lens Characteristics and Image Formation
- is the bending of light as it passes through a lens, governed by the
- determines how much light bends when entering or exiting a lens
- can occur in lenses, causing distortions in the image
- results in different colors of light being refracted at slightly different angles
Key Terms to Review (27)
Aberration: Aberration refers to the distortion or deviation in the image produced by optical systems, such as lenses or microscopes. This distortion can lead to imperfections in the clarity and focus of an image, affecting its overall quality. Understanding aberrations is crucial for optimizing image formation and achieving clearer observations in various applications.
Central Ray: The central ray is a key concept in the study of image formation by lenses. It is a hypothetical ray of light that passes through the center of a lens and undergoes minimal refraction, serving as a reference point for understanding how other rays of light interact with the lens.
Chromatic Dispersion: Chromatic dispersion is the phenomenon where different wavelengths of light travel at different velocities within a medium, causing the light to separate into its constituent colors. This effect is particularly prominent in optical fibers and lenses, and it can have significant implications for the formation of images.
Concave Lens: A concave lens is a type of diverging lens that is thinner at the center and thicker at the edges. This lens causes light rays to bend outward, resulting in a negative focal length and the formation of a virtual, diminished, and upright image.
Converging (or convex) lens: A converging (or convex) lens is a lens that causes parallel rays of light to converge at a single point called the focal point. It is thicker in the middle than at the edges.
Convex Lens: A convex lens is a type of optical lens that is thicker at the center than at the edges. It is able to converge or focus light rays, allowing it to form real, inverted images of objects placed in front of it.
Diopter: A diopter is a unit of measurement used to describe the optical power or refractive power of a lens or curved surface. It is the reciprocal of the focal length of the lens, measured in meters, and is used to quantify the degree of convergence or divergence of light passing through the lens.
Diverging lens: A diverging lens, often called a concave lens, is a lens that causes parallel rays of light to spread out (diverge) after passing through it. Diverging lenses have at least one surface that curves inward.
Focal point: The focal point is the specific point where light rays parallel to the principal axis converge after passing through a lens or reflecting off a mirror. It is crucial for understanding image formation in optical systems.
Focal Point: The focal point is the point at which light rays converge or diverge after passing through a lens or reflecting off a curved mirror. It is the location where an image is formed in an optical system.
Focal Ray: A focal ray is a light ray that passes through the focal point of a lens or mirror. It is a key concept in understanding the formation of images by optical devices, such as lenses and mirrors, and is essential for analyzing the behavior of light in these systems.
Image distance: Image distance is the distance between the image formed by a lens and the lens itself. It is usually denoted by $d_i$ and can be positive or negative depending on the type of image formed.
Index of refraction: The index of refraction, or refractive index, is a dimensionless number that describes how light propagates through a medium. It is defined as the ratio of the speed of light in a vacuum to its speed in the specified medium.
Index of Refraction: The index of refraction, also known as the refractive index, is a dimensionless number that describes how light propagates through a particular medium. It is a fundamental property of a material that determines the speed of light within that material and the degree to which light is bent, or refracted, when it passes from one medium to another.
Lens Equation: The lens equation is a fundamental relationship that describes the formation of images by a lens. It establishes a connection between the object distance, image distance, and the focal length of a lens, allowing for the prediction and analysis of image properties in optical systems.
Magnification: Magnification is the measure of how much larger or smaller an image is compared to the object itself. It is given by the ratio of the image height to the object height.
Magnification: Magnification is the process of enlarging the apparent size of an object or image, making it appear larger than its actual size. This concept is crucial in understanding the formation of images by various optical devices, such as lenses, mirrors, microscopes, and telescopes.
Optical Axis: The optical axis is an imaginary line that passes through the center of a lens or mirror and is perpendicular to the surface. It is the principal axis along which light travels and is the reference point for image formation in optical systems.
Parallel Ray: A parallel ray is a ray of light that travels in a straight line and maintains a constant distance from other parallel rays. These rays are parallel to each other, meaning they never converge or diverge, and they are often used in the context of image formation by lenses.
Power: Power is the rate at which work is done or energy is transferred over time. It is measured in watts (W), where one watt equals one joule per second.
Real image: A real image is formed when light rays converge at a point after passing through a lens or reflecting from a mirror. It can be projected onto a screen as the light actually passes through the image location.
Real Image: A real image is a type of image that is formed by the actual convergence of light rays from an object. It can be captured on a screen or photographic film and is considered a true representation of the object being imaged.
Refraction: Refraction is the bending of a wave, such as light or sound, when it passes from one medium to another with a different density or refractive index. This phenomenon occurs due to the change in the speed of the wave as it moves between the two mediums, causing it to change direction.
Thin Lens: A thin lens is an optical lens where the thickness of the lens is negligible compared to the radius of curvature of its surfaces. This allows for simplified analysis and calculations of the image formation properties of the lens.
Thin lens equations: Thin lens equations relate the focal length of a lens to the distances of the object and the image from the lens. These equations are fundamental in determining image formation by lenses.
Virtual image: A virtual image is an image formed by rays that appear to converge but do not actually meet. It cannot be projected onto a screen because the light rays only seem to come from the image location.
Virtual Image: A virtual image is an image that appears to exist in a different location than the actual object, but does not physically exist in that location. It is an image that is formed when light rays diverge or appear to diverge from a point, but do not actually intersect at that point.