File:Gravitational lens geometry.svg
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Summary
Optical geometry of a <a href="https://en.wikipedia.org/wiki/gravitational_lens" class="extiw" title="w:gravitational lens">gravitational lens</a> where,
- <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:1.498ex; height:1.676ex;" alt="\alpha "> is the bending angle,
- <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0000814c4098b528fd04b02574d5d56e2779b25b" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.671ex; width:2.401ex; height:2.509ex;" alt="\theta _{S}"> is the actual angle subtended (without lens effect) by the source at the observer,
- <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f84b9443d095623e02fd287cd095123d70b0278" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.671ex; width:2.163ex; height:2.509ex;" alt="\theta _{1}"> is the observed angle subtended (due to lens effect) by the apparent source at the observer,
- <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e44b39c353d4634b76f550679dcc7aed38a0cd47" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.671ex; width:3.294ex; height:2.509ex;" alt="D_{L}"> is the <a href="https://en.wikipedia.org/wiki/angular_diameter_distance" class="extiw" title="w:angular diameter distance">angular diameter distance</a> to the lens,
- <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec66bd07fe0649713f001c8a0af2fd5dca47c6d9" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.671ex; width:3.234ex; height:2.509ex;" alt="D_{S}"> is the angular diameter distance to the source, and
- <img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d097eff5bae416f31ad8c71dbf5e65d78970e9c" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.671ex; width:4.361ex; height:2.509ex;" alt="D_
"> is the angular diameter distance between the lens and the source.Works by Lemony Snicket
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File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 19:02, 16 January 2017 | | 512 × 307 (2 KB) | 127.0.0.1 (talk) | Optical geometry of a <a href="https://en.wikipedia.org/wiki/gravitational_lens" class="extiw" title="w:gravitational lens">gravitational lens</a> where, <br><dl> <dd> <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>α<!-- α --></mi></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.338ex; width:1.498ex; height:1.676ex;" alt="\alpha "></span> is the bending angle,</dd> <dd> <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>θ<!-- θ --></mi><mrow class="MJX-TeXAtom-ORD"><mi>S</mi></mrow></msub></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \theta _{S}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0000814c4098b528fd04b02574d5d56e2779b25b" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.671ex; width:2.401ex; height:2.509ex;" alt="\theta _{S}"></span> is the actual angle subtended (without lens effect) by the source at the observer,</dd> <dd> <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>θ<!-- θ --></mi><mrow class="MJX-TeXAtom-ORD"><mn>1</mn></mrow></msub></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle \theta _{1}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f84b9443d095623e02fd287cd095123d70b0278" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.671ex; width:2.163ex; height:2.509ex;" alt="\theta _{1}"></span> is the observed angle subtended (due to lens effect) by the apparent source at the observer,</dd> <dd> <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>D</mi><mrow class="MJX-TeXAtom-ORD"><mi>L</mi></mrow></msub></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle D_{L}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e44b39c353d4634b76f550679dcc7aed38a0cd47" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.671ex; width:3.294ex; height:2.509ex;" alt="D_{L}"></span> is the <a href="https://en.wikipedia.org/wiki/angular_diameter_distance" class="extiw" title="w:angular diameter distance">angular diameter distance</a> to the lens,</dd> <dd> <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>D</mi><mrow class="MJX-TeXAtom-ORD"><mi>S</mi></mrow></msub></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle D_{S}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec66bd07fe0649713f001c8a0af2fd5dca47c6d9" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.671ex; width:3.234ex; height:2.509ex;" alt="D_{S}"></span> is the angular diameter distance to the source, and</dd> <dd> <span><span class="mwe-math-mathml-inline mwe-math-mathml-a11y mw-math-element" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><msub><mi>D</mi><mrow class="MJX-TeXAtom-ORD"><mi>L</mi><mi>S</mi></mrow></msub></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle D_{LS}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4d097eff5bae416f31ad8c71dbf5e65d78970e9c" class="mwe-math-fallback-image-inline mw-math-element" aria-hidden="true" style="vertical-align: -0.671ex; width:4.361ex; height:2.509ex;" alt="D_{{LS}}"></span> is the angular diameter distance between the lens and the source.</dd> </dl> |
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