Thin Convex Lens

xConvex lenses are thin, curved lenses that are thicker at the centre and thinner at the edges. Convex lenses cause parallel rays of light to converge to a single point as they pass through the lens. The focal length of all concave lenses is positive.

Example Convex Lens

<defs> <style class="style-fonts"> @font-face { font-family: "Virgil"; src: url("https://excalidraw.com/Virgil.woff2"); } @font-face { font-family: "Cascadia"; src: url("https://excalidraw.com/Cascadia.woff2"); } @font-face { font-family: "Assistant"; src: url("https://excalidraw.com/Assistant-Regular.woff2"); } </style>

</defs> <rect x="0" y="0" width="142.2872044181604" height="306.37823679726574" fill="#ffffff"/><g stroke-linecap="round"><g transform="translate(110.39906569827781 16.64023407297725) rotate(0 -37.31490260739287 137.81968172075435)" fill-rule="evenodd"><path d="M-60.15 -1.94 C-60.15 -1.94, -60.15 -1.94, -60.15 -1.94 M-60.15 -1.94 C-60.15 -1.94, -60.15 -1.94, -60.15 -1.94 M-61.99 12.37 C-58.29 9.1, -56.71 4.43, -49.52 -1.97 M-61.99 12.37 C-57.54 7.93, -52.97 2.58, -49.52 -1.97 M-64.48 27.42 C-60.35 19.18, -52.5 12.71, -38.89 -2.01 M-64.48 27.42 C-57.59 18.58, -48.57 9.14, -38.89 -2.01 M-66.31 41.73 C-51.36 24.62, -38.44 10.09, -28.92 -1.29 M-66.31 41.73 C-54.47 29.08, -42.94 15.7, -28.92 -1.29 M-68.81 56.79 C-53.37 37.14, -32.12 14.57, -18.29 -1.32 M-68.81 56.79 C-56.38 41.72, -42.54 25.72, -18.29 -1.32 M-70.64 71.09 C-52.07 52.58, -35.45 31.01, -14.88 6.94 M-70.64 71.09 C-54.26 53.03, -38.34 33.62, -14.88 6.94 M-73.13 86.15 C-59.47 70.77, -42.95 50.72, -12.12 15.97 M-73.13 86.15 C-59.16 71.21, -46.42 56.19, -12.12 15.97 M0.35 1.63 C0.48 1.36, 0.76 1.13, 1 0.87 M0.35 1.63 C0.58 1.4, 0.7 1.17, 1 0.87 M-74.97 100.46 C-56.33 80.94, -39.88 61.26, -9.36 24.99 M-74.97 100.46 C-60.29 82.78, -46.84 66.9, -9.36 24.99 M0.48 13.67 C2 12.35, 2.88 10.27, 5.07 8.38 M0.48 13.67 C2.02 11.64, 3.59 9.83, 5.07 8.38 M-77.46 115.52 C-63.02 96.81, -48.41 80.22, -6.6 34.01 M-77.46 115.52 C-63.63 100.32, -49.25 83.37, -6.6 34.01 M0.61 25.71 C0.86 25.48, 1.01 25.39, 1.27 24.95 M0.61 25.71 C0.87 25.44, 1.12 25.21, 1.27 24.95 M-79.29 129.82 C-53.77 99.89, -24.73 69.22, -3.19 42.28 M-79.29 129.82 C-55.74 104.08, -30.8 76.19, -3.19 42.28 M-2.53 41.52 C-1.82 40.95, -0.42 39.31, 1.4 36.99 M-2.53 41.52 C-1.84 40.75, -0.66 39.74, 1.4 36.99 M-78.5 141.11 C-61.61 120.19, -46.85 101.66, 1.54 49.04 M-78.5 141.11 C-50.02 107.29, -21.49 74.92, 1.54 49.04 M-77.06 151.64 C-45.82 118.36, -19.74 84.54, 1.67 61.08 M-77.06 151.64 C-50.22 119.27, -22 88.38, 1.67 61.08 M-75.61 162.17 C-45.37 131.27, -19.46 95.49, 1.8 73.12 M-75.61 162.17 C-45.35 127.56, -15.45 93.76, 1.8 73.12 M-73.51 171.95 C-44.33 139.52, -16.33 108.58, 2.59 84.4 M-73.51 171.95 C-47.8 142.01, -21.29 111.53, 2.59 84.4 M-72.07 182.48 C-51.48 160.91, -32.29 137.15, 2.72 96.44 M-72.07 182.48 C-51.98 158.38, -33.01 136.72, 2.72 96.44 M-70.62 193.01 C-50.05 168.51, -31.81 146.05, 2.86 108.49 M-70.62 193.01 C-52.48 170.82, -31.96 149.31, 2.86 108.49 M-69.18 203.54 C-41.84 171.26, -14.67 139.59, 2.99 120.53 M-69.18 203.54 C-43.87 174.66, -17.13 145.43, 2.99 120.53 M-67.73 214.08 C-42.11 185.74, -20.14 158.18, 3.78 131.81 M-67.73 214.08 C-52 196.02, -36.67 179.27, 3.78 131.81 M-66.29 224.61 C-46.72 205.97, -31.23 182.83, 2.6 145.36 M-66.29 224.61 C-51.79 208.36, -37.74 191.21, 2.6 145.36 M-64.84 235.14 C-46.54 215.64, -27.91 194.22, 0.11 160.42 M-64.84 235.14 C-43.56 208.72, -19.33 183.44, 0.11 160.42 M-62.74 244.91 C-43.94 220.89, -25.5 201.36, -2.38 175.48 M-62.74 244.91 C-47.81 226.36, -30.42 207.63, -2.38 175.48 M-61.29 255.45 C-42.83 237.25, -28.38 217.95, -5.53 191.3 M-61.29 255.45 C-47.82 239.45, -34.44 223.77, -5.53 191.3 M-59.85 265.98 C-49.95 254.53, -38.98 242.75, -8.02 206.36 M-59.85 265.98 C-39.03 242.62, -20.5 219.95, -8.02 206.36 M-58.4 276.51 C-46.17 263.02, -36.14 251.54, -11.17 222.17 M-58.4 276.51 C-40.92 257.88, -23.8 236.91, -11.17 222.17 M-48.43 277.23 C-38.18 267.92, -30.2 255.74, -13.66 237.23 M-48.43 277.23 C-38.63 267.38, -29.66 254.87, -13.66 237.23 M-37.8 277.2 C-28.24 268.38, -22.84 258.34, -16.8 253.04 M-37.8 277.2 C-29.49 268.93, -23.41 260.38, -16.8 253.04 M-26.51 276.41 C-24.05 274.41, -22.57 272.51, -19.3 268.1 M-26.51 276.41 C-24.84 274.65, -22.72 272.02, -19.3 268.1" stroke="DimGray" stroke-width="1" fill="none"/><path d="M0 0 C0.36 50.72, 1.31 97.94, 3.44 141.16 M0 0 C2.8 52.49, 2.99 104.63, 3.44 141.16 M3.44 141.16 C-2.1 171.33, -5.72 203.18, -20.76 275.79 M3.44 141.16 C-1.83 173.29, -8.62 205.98, -20.76 275.79 M-20.76 275.79 C-27.36 274.48, -39.18 277.64, -58.58 277.68 M-20.76 275.79 C-34.07 275.96, -47.39 277.42, -58.58 277.68 M-58.58 277.68 C-62.59 241.39, -68.72 206.35, -79.83 132.84 M-58.58 277.68 C-65.82 231.03, -71.75 186.01, -79.83 132.84 M-79.83 132.84 C-73.12 81.53, -62.29 27.81, -60.07 -2.04 M-79.83 132.84 C-75.27 103.6, -71.19 76.23, -60.07 -2.04 M-60.07 -2.04 C-46.96 -1.95, -36.12 -3.12, -17.83 -1.38 M-60.07 -2.04 C-49.18 -0.69, -38 -0.76, -17.83 -1.38 M-17.83 -1.38 C-13.74 7.31, -13.25 17.27, -3.51 43.72 M-17.83 -1.38 C-14.77 7.86, -12.53 16.95, -3.51 43.72 M-3.51 43.72 C-1.27 31.53, 0.54 19.76, 5.2 5.81 M-3.51 43.72 C0.04 30.83, 2.87 18.9, 5.2 5.81 M5.2 5.81 C4.23 4.53, 1.3 1.73, 0 0 M5.2 5.81 C3.95 4.33, 2.42 2.56, 0 0" stroke="transparent" stroke-width="2" fill="none"/></g></g><mask/><g stroke-linecap="round"><g transform="translate(52.16098565857031 10.931328671566718) rotate(0 22.846228943832422 0)"><path d="M0.3 -0.16 C7.99 -0.14, 38.71 0.05, 46.23 0.16 M-0.2 -0.72 C7.45 -0.88, 38.55 -0.79, 46.08 -0.72" stroke="#1e1e1e" stroke-width="2" fill="none"/></g></g><mask/><g stroke-linecap="round"><g transform="translate(51.07334179075758 295.8789588037879) rotate(0 22.155539437612276 0)"><path d="M0.54 0.16 C7.83 0.27, 36.83 0.47, 44.06 0.5 M0.15 -0.23 C7.33 -0.25, 36.02 -0.15, 43.51 -0.21" stroke="#1e1e1e" stroke-width="2" fill="none"/></g></g><mask/><g stroke-linecap="round"><g transform="translate(51.71315371605877 11.206074289642629) rotate(0 -11.491692804797722 142.0617629572108)"><path d="M1.11 0.02 C-2.92 23.72, -22.88 95.47, -23.22 142.69 C-23.55 189.91, -4.84 259.94, -0.91 283.34 M0.24 -1.01 C-4.05 22.81, -24.5 96.44, -24.29 143.98 C-24.07 191.53, -2.68 260.97, 1.51 284.25" stroke="#1e1e1e" stroke-width="2" fill="none"/></g></g><mask/><g stroke-linecap="round" transform="translate(106.60813438040947 12.677557029947081) rotate(345.8655104653645 8.445116077140227 37.03749807299232)"><path d="M-0.49 0.09 L17.31 -0.16 L17.5 74.73 L-0.75 73.72" stroke="none" stroke-width="0" fill="#ffffff"/><path d="M0 0 C5.35 -0.6, 9.26 0.66, 16.89 0 M0 0 C6.38 0.25, 13.17 -0.02, 16.89 0 M16.89 0 C16.59 29.01, 17.16 58.89, 16.89 74.07 M16.89 0 C16.96 19.68, 16.49 39.98, 16.89 74.07 M16.89 74.07 C14.05 74.68, 10.25 74.09, 0 74.07 M16.89 74.07 C10.45 74.38, 3.54 74.09, 0 74.07 M0 74.07 C-0.5 48.43, -0.76 21.13, 0 0 M0 74.07 C0.23 53.19, 0.03 32.95, 0 0" stroke="#ffffff" stroke-width="2" fill="none"/></g><g stroke-linecap="round"><g transform="translate(96.9899664405703 10.300315151261202) rotate(0 11.491692804797722 142.0617629572108)"><path d="M0.95 0.49 C4.97 24.5, 24.29 95.98, 24.1 143.18 C23.9 190.37, 3.93 260.3, -0.23 283.66 M0 -0.3 C3.95 23.99, 23.92 97.22, 23.73 144.73 C23.54 192.23, 3.02 261.52, -1.12 284.74" stroke="#1e1e1e" stroke-width="2" fill="none"/></g></g><mask/><g stroke-linecap="round" transform="translate(10 137.94667912861337) rotate(0 5.7045440673828125 13.547752380371094)"><path d="M6.8 0.98 L11.55 13.27 L6.68 26.72 L-0.8 13.41" stroke="none" stroke-width="0" fill="#ffffff" fill-rule="evenodd"/><path d="M6 0 C6.92 2.7, 8.16 5.52, 11.41 14 M6 0 C7.31 4.27, 9.28 8.68, 11.41 14 M11.41 14 C8.99 18.57, 8.48 23.22, 6 27.1 M11.41 14 C10.07 17.16, 8.58 20.36, 6 27.1 M6 27.1 C3.99 24.34, 2.7 20.67, 0 14 M6 27.1 C4.84 23.78, 3.33 20.92, 0 14 M0 14 C2.58 9.11, 4.1 5.42, 6 0 M0 14 C1.43 10.66, 3.08 7.86, 6 0" stroke="#ffffff" stroke-width="2" fill="none"/></g></svg>

Example of a convex lens

The focal length, image position, and object position are all related through the thin lens equations