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Diffuse lighting meaningin physics

A lens is a device designed to refract, or bend, light in a specific way to create an image. Lenses cause light to refract twice, once when it enters the lens and again when it leaves. The focal length (denoted by lowercase f) describes how a lens refracts light and can be used to calculate a lens's magnification using the formula m = -i/o, with positive magnification indicating an upright image and negative magnification indicating an inverted image. The Thin Lens Equation states that 1/f = 1/o + 1/i, and is used in conjunction with the magnification equation to determine where a lens will create an image.

DiffusedlightingExamples

To perform diffuse lighting calculations each vertex that defines a triangle must have an associated normal vector. The normal vector defines a direction that is projecting out from the front side of the triangle. The normal vector defines how light will reflect off of a surface defined at the vertex. The normal vector may be 90 degrees to the surface of the triangle, or it might be at some other angle to simulate a curved surface.

Chromatic aberration occurs when a lens fails to focus all wavelengths of light to a single point. This is due to the variation in refractive index for different wavelengths, causing colors to separate and resulting in image distortion or color fringing. Spherical aberration occurs when light rays passing through the periphery of a lens focus at different points than those passing through its center. This results in image blurring. Both chromatic and spherical aberrations can degrade optical performance and reduce image clarity if not corrected using specialized lens designs or material combinations.

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The dot product of two vectors is defined as the sum of the products of their associated terms. 3D vectors are normally stored as arrays, where (v[0], v[1], v[2]) is the values of the vector. Therefore, the dot product of vectors v0 and v1 is:

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The Thin Lens Equation is a fundamental formula used in optics to relate the focal length, object distance, and image distance for a lens. It is given by 1/f = 1/o + 1/i, where f is the focal length, o is the object distance, and i is the image distance. This equation is useful for calculating one of the variables when the other two are known, allowing for the analysis of lens systems and the prediction of image formation in various optical applications.

Converging lenses, also known as convex lenses, are thicker in the middle and thinner at the edges. They cause parallel light rays to converge or focus at a single point called the focal point. Diverging lenses, also known as concave lenses, are thinner in the middle and thicker at the edges. They cause parallel light rays to diverge or spread out, making them appear as if they are originating from a single focal point on the other side of the lens.

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Focal length is the distance from the lens at which parallel light rays converge (for converging lenses) or appear to diverge from (for diverging lenses). It is inversely proportional to the lens's power, which is measured in diopters (D). A lens with a longer focal length has a lower power and vice versa.

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There are two major types of lenses: converging and diverging. Converging lenses have a positive focal length and converge light rays, while diverging lenses have a negative focal length and spread light rays apart. Lenses are commonly used in vision correction, and the power of a lens can be calculated using the inverse of the focal length. The human eye contains two lenses—the cornea and the lens—which work together to form sharp images on the retina. Imperfections in lenses can lead to chromatic aberration and spherical aberration, both causing image distortion.

The example WebGL program above was based on a “point light source”. If you had a different type of light source, such as a sun light source, the shader programs would have to be changed because the definition of your light source would change, but the fundamental math would be the same.

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• Introduction to lenses and their effects on light
• Focal length (f)
• The Thin Lens Equation: 1/f = 1/o + 1/i
• Magnification equation: -i/o
• Sign conventions for distances and magnification
• Positive object distance: Object located on the same side as the light source
• Positive image distance: Image formed on the side opposite to the light source
• Negative image distance: Image formed on the same side as the light source
• Positive magnification: Upright image orientation
• Negative magnification: Inverted image orientation
• Types of lenses
  • Converging lenses (positive focal length, convex)
  • Diverging lenses (negative focal length, concave)
• Vision correction
  • Power (diopters) = 1/f
  • Hyperopia (farsightedness), corrected by converging lenses
  • Myopia (nearsightedness), corrected by diverging lenses
• Human eye lenses: cornea and lens
• Multiple lens systems
  • Total power and magnification
• Imperfections in images generated by lenses
  • Chromatic aberration
  • Spherical aberration

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The diagram to the right labels the pieces needed to calculate diffuse reflection. We need to calculate the angle between the vertex’s normal vector and a vector pointing at the light source from the vertex. This angle is labeled “theta” in the diagram.

Diffused light photography Examples

If both v0 and v1 are normal vectors that have a length of 1, the dot product gives the cosine of the angle without any division.

Light that directly strikes an object and then reflects in all directions is called “diffuse” light. The amount of light reflection is determined by the angle between the light ray and the surface normal vector. In Physics, Lambert’s cosine law provides an equation for calculating diffuse color.

Magnification is the ratio of the size of an image produced by a lens to the size of the object being imaged. It is calculated as the image distance (i) divided by the object distance (o), or m = -i/o. Positive magnifications imply upright images, and negative magnifications imply inverted images. Magnification depends on the properties of the lens, the object distance, and image distance. Converging lenses can create both real and virtual images with positive or negative magnifications, whereas diverging lenses always create virtual images with negative magnification (objects appear smaller).

It can be shown that the dot product of two vectors is equal to the cosine of the angle between the two vectors divided by the length of the two vectors. In code format, this means that:

Diffused light photography

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Examine the plot of a cosine curve to the right. Notice that when the angle is zero, the cosine of zero is 1.0. As the angle increases, the cosine of the angle curves to zero. When the angle is 90 degrees, the cosine of 90 is 0.0. This is lambert’s cosine law. The cosine values are treated as percentages of color. When the angle is zero, cos(0) is 1.0, and you get 100% color. When the angle is 90 degrees, cos(90) is zero and you get 0% color. When the angle becomes greater than 90 or less than -90 the cosine goes negative. This is an indication that the front side of the triangle is pointing away from the light source. You can’t have a negative percentage of light, so we clamp the cosine of the angle to values between 0.0 and 1.0.

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As you experiment with the demonstration program, please make sure you observe the following characteristics of diffuse reflection.