#dispersion

Telescope, Human Eye and Defects of Vision

A prism of angle \( 45^\circ \) and refractive index \( 1.6 \) produces what minimum deviation?

**Telescope resolving power** depends on objective aperture, magnification limited by objective diffraction, terrestrial telescope adds erecting lens, Galilean uses diverging eyepiece for erect image, reflecting telescope uses concave mirror objective avoiding chromatic aberration. For a thin prism: D_m = (n - 1) A . n = 1.6 , A = 45° . D_m = (1.6 - 1) × 45 = 0.6 × 45 = 27° . Substituting values gives 27°, which matches expected image position and magnification from mirror/lens formula 1/f = 1/v - 1/u (lens) or 1/f = 1/v + 1/u (mirror), confirming sign conventions and refraction principles.

Ref: NCERT > Physics Book > Ray Optics > Telescope, Human Eye and Defects of Vision

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Refraction Through Prism and Minimum Deviation

Why does a prism disperse white light into a spectrum of colors?

**Refraction through prism** deviation δ = i+e-A, minimum when i=e, symmetrical path, r₁=r₂=A/2, n = sin[(A+δ_m)/2]/sin(A/2). In water n_rel = n_prism/n_water =1.5/1.33=1.128, so δ_m reduces because relative index lower, new δ_m from formula with n_rel. A prism disperses white light because different wavelengths (colors) of light have different refractive indices in the prism material. Shorter wavelengths (e.g., violet) refract more than longer wavelengths (e.g., red), causing the light to split into a spectrum as it exits the prism. Substituting values gives Due to different refractive indice

Ref: NCERT > Physics Book > Ray Optics > Refraction Through Prism and Minimum Deviation

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Population Ecology

Dispersion of individuals due to lack of interaction results in:

“Random dispersion” for dispersion of individuals due to lack of interaction results in. This relationship follows from the ecological mechanism represented by the terms in the item, not merely from an association between their names. Population ecology links individual births, deaths, immigration, and emigration to changes in abundance. Per-capita rates determine the direction of change, while density dependence creates feedback when crowding alters survival or reproduction. The remaining alternatives—“Clumped dispersion”, “Uniform dispersion”, “Clustered dispersion”—refer to different states

Ref: Campbell Biology, Urry et al., 12th Ed., Unit 8 Ecology

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Density Dispersion Meta pop

A ratio of variance to mean > 1 indicates:

The variance-to-mean ratio, often called an index of dispersion, compares observed variation among equal sampling units with the Poisson expectation. Randomly and independently placed individuals yield a ratio near 1 because a Poisson distribution has equal mean and variance. A ratio greater than 1 indicates overdispersion: counts differ more among quadrats than chance alone predicts, with many low-count units and some high-count units. This is the statistical signature of clumping. Patchy resources, social attraction, restricted dispersal, and reproduction near parents can all generate it. Un

Ref: Ecology: Concepts and Applications, Molles, 9th Ed., Ch. 9

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Density Dispersion Meta pop

Dispersion where individuals aggregate in patches is:

Clumped dispersion occurs when individuals are concentrated in groups or habitat patches rather than spaced independently or evenly. It is the most common broad pattern in nature because resources such as water, nutrients, shelters, hosts, or breeding sites are often spatially heterogeneous. Limited dispersal can keep offspring near parents, and social processes such as flocking, schooling, colony formation, or cooperative defense can further promote aggregation. In quadrat data, clumping typically produces variance greater than the mean: many units contain few or no individuals, while a small

Ref: Ecology: Concepts and Applications, Molles, 9th Ed., Ch. 9

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Population Growth

Which type of dispersion is indirectly modeled in logistic growth?

The nonspatial logistic equation models only change in total abundance and contains no variables for the positions or spacing of individuals. It therefore does not indirectly specify uniform dispersion, and the keyed response is scientifically inconsistent. Random, clumped, or uniform patterns require spatial data or an explicitly spatial model involving movement, local interactions, or habitat heterogeneity. Parameters have clear roles: N is current abundance, r is the maximum per-capita rate under the model, and K is the positive equilibrium set by environmental capacity. The term 1 - N/K su

Ref: Ecology: Concepts and Applications, Molles, 9th Ed., Ch. 11

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