Radius of curvature divided by tube diameter.
To get the radius of curvature, imaging the bend in the tube is a segment of a circle, the radius of curvature is the radius of that circle.
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The radius of curvature of a circle, or an arc of a circle is the same as the radius of the circle.
For a curve (other than a circle) the radius of curvature at a given point is obtained by finding a circular arc that best fits the curve around that point. The radius of that arc is the radius of curvature for the curve at that point.
The radius of curvature for a straight line is infinite.
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Curvature is a general term to describe a graph. Like, concave or convex.
Radius of curvature is more exact. If the curve in a 'small' section is allow to continue with the same curvature it would form a circle. that PRETEND circle would have an exact radius. That is the radius of curvature.
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The radius of the sphere of which a lens surface or curved mirror forms a part is called the radius of curvature.
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radius of curvature = 2Focal length
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The radius of curvature is the distance from the center of a curved surface or lens to a point on the surface, while the center of curvature is the point at the center of the sphere of which the curved surface is a part. In other words, the radius of curvature is the length of the line segment from the center to the surface, while the center of curvature is the actual point.
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There is a specific formula for finding the radius of a curvature, used often when one is measuring a mirror. The formula is: Radius of curvature = R =2*focal length.
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The radius of curvature of a lens is the distance between the center of the lens and its focal point. It is a measure of the curvature of the lens surface. A smaller radius of curvature indicates a more curved lens, while a larger radius indicates a flatter lens.
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The radius of curvature and the focal length mean the same so the radius of curvature is also 15 cm.
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The radius of curvature is given by
(1)
where is the curvature. At a given point on a curve, is the radius of the osculating circle. The symbol is sometimes used instead of to denote the radius of curvature (e.g., Lawrence 1972, p. 4).
Let and be given parametrically by
(2)(3)
then
(4)
where and . Similarly, if the curve is written in the form , then the radius of curvature is given by
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The curvature of the radius of a lens affects its focal length and optical power. A lens with a shorter radius of curvature will have a shorter focal length and higher optical power, while a lens with a larger radius of curvature will have a longer focal length and lower optical power.
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When the curvature radius is larger, the focal point moves closer to the lens or mirror. This is because the curvature radius affects the focal length – a larger radius results in a shorter focal length and thus a closer focal point.
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1/a
According to Wikipedia,
"The canonical example of extrinsic curvature is that of a circle, which has curvature equal to the inverse of its radius everywhere. Smaller circles bend more sharply, and hence have higher curvature. The curvature of a smooth curve is defined as the curvature of its osculating circle at each point."
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No, the focal length and radius of curvature of a lens cannot be the same. The radius of curvature is twice the focal length for a lens. This relationship is based on the geometry of the lens and the way light rays converge or diverge when passing through it.
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The curvature of the Earth in any direction can be calculated using the formula for the Earth's radius of curvature (R), which is given by R = a / √(1 - e^2sin²φ) where a is the equatorial radius of the Earth and e is the eccentricity of the Earth. By determining the radius of curvature at a specific latitude (φ), you can find the curvature in that direction.
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A plane mirror is not curved so it does not have a center of curvature. Or if you want to be mathematically correct, you could say that it's center of curvature is at an infinite distance from the mirror.
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radius of curvature is double of focal length.
therefore, the formula is:
1/f = (n-1)[ 1/R1 - 1/R2 + (n-1)d/nR1R2]
here f= focal length
n=refractive index
R1=radius of curvature of first surface
R2=radius of curvature of 2nd surface
d=thickness of the lens
using this, if you know rest all except one, then you can calculate that.
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The lens power increases as the curvature of the lens surface becomes steeper. A lens with a larger radius of curvature will have a lower power, while a lens with a smaller radius of curvature will have a higher power. This relationship is described by the lensmaker's equation, which relates the power of a lens to the refractive index of the lens material and the radii of curvature of its surfaces.
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The focal point of a convex mirror lies on the same side as the centre of curvature and is at a distance of half the radius of curvature from the optical centre.
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The relation between focal length (f), radius of curvature (R), and the focal point of a spherical mirror can be described by the mirror equation: 1/f = 1/R + 1/R'. The focal length is half the radius of curvature, so f = R/2.
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The average radius of curvature of the cornea in a human eye is approximately 7.8 mm. This curvature plays a crucial role in focusing light onto the retina for clear vision. Changes in the radius of curvature can affect the eye's refractive power and lead to vision problems like nearsightedness or farsightedness.
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The formula for the radius of curvature (R) of a double convex lens is given by R = 2f, where f is the focal length of the lens. The radius of curvature is the distance from the center of the lens to the center of curvature of one of its curved surfaces.
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The focal length of a concave mirror is about equal to half of its radius of curvature.
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Radius of curvature in Newton's rings is the radius of the curvature of the wavefront at the point where interference fringes are observed. It is calculated by measuring the diameter of the nth dark ring and using the formula R = (n * λ * D) / (2 * δ), where R is the radius of curvature, n is the order of the ring, λ is the wavelength of light, D is the distance between the lens and the glass plate, and δ is the diameter of the nth dark ring.
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The curvature of a lens refers to the amount of bending in the lens surface. A lens can have a convex curvature (outward bending) or a concave curvature (inward bending), which affects how it refracts light. Curvature is measured by the radius of curvature, which can determine the focal length and strength of the lens.
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A lens with a large radius of curvature allows for a greater region of interference fringes to be observed, making it easier to measure the diameter of the rings accurately. This increases the precision of the experiment and reduces errors in measurement. Additionally, a large radius of curvature reduces the curvature of the lens surfaces, leading to more uniform and symmetrical interference patterns.
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Tangent continuity: No sharp angles.
Curvature continuity: No sharp radius changes.
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The center of curvature of a lens is the point located at a distance equal to the radius of curvature from the center of the lens. It is the point where the principal axis intersects the spherical surface of the lens.
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The Center of curvature is 2 times the focal length.
By the way this is a physics question.
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Given a set of x and y coordinates, fit a curve to it using statistical techniques. The radius of curvature for the set of points is the radius of curvature for this arc. To find that, the curve must be differentiable twice. Let the curve be represented by the equation y = y(x) and let y' and y" be the first and second derivatives of y(x) with respect to x.
Then R = abs{(1 + y'^2)^(3/2) / y"} is the radius of curvature.
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By increasing its radius of curvature to infinity.
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Its radius of curvature and its reflecting property
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It is the distance, from any point on a curve, to the centre of curvature at that point.
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There is not enough information to answer the question.
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Radius of rings is directly proportional to the square root of the radius of curvature. Thin lens would have larger radius of curvature and hence the option
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The curvature of a convex lens refers to the amount of curvature or bend present on each of its surfaces. It is typically defined by the radius of curvature, which indicates how sharply the lens surface is curved. This curvature plays a significant role in determining the focal length and optical properties of the lens.
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The focal length of a lens is related to its radius of curvature and the index of refraction by the lensmaker's equation: [\frac{1}{f} = (n-1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right)] Given the radius of curvature (R = 0.70 , m) and the index of refraction (n = 1.8), you can calculate the focal length.
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The focal length of a mirror with a radius of curvature of 40.5 cm is half of the radius, so it is 20.25 cm. The mirror's face would be placed around this focal length distance from the person's face for optimal viewing.
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If the image produced is 4 times the size of the object and inverted, then the object is placed at a distance equal to half the radius of curvature from the mirror. This would position the object beyond the center of curvature of the concave mirror. Using an accurate scale, you would measure a distance of half the radius of curvature from the mirror to locate the object.
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There is no such expression. The normal to a surface, at a given point is the radius of curvature of the surface, at that point.
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You need to do your differentiation in terms of polar coordinates
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In a large curvature lens radius, the focal point moves further away from the lens. This means that the focal length increases, resulting in the light rays converging to a point further from the lens surface.
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A spherometer is a measuring instrument used to determine the curvature, or radius of curvature, of a spherical surface. It consists of three legs resting on the surface being measured, with a central screw that can be adjusted to touch the surface at its center. The principle of operation is based on measuring the change in height of the central leg when the screw is adjusted, allowing calculation of the radius of curvature.
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It is positive for one surface, negative for the other. Subject to that, the radii can have have any values.
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For a convex mirror, the focal length (f) is half the radius of curvature (R) of the mirror. This relationship arises from the mirror formula for convex mirrors: 1/f = 1/R + 1/v, where v is the image distance. When the object is at infinity, the image is formed at the focal point, and the image distance is equal to the focal length. Hence, 1/f = -1/R when solving for the focal length in terms of the radius of curvature for a convex mirror.
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