The graph between $\frac{1}{u}and\frac{1}{v}$ for a thin convex lens in order to determine its focal length is plotted as shown in the figure. The refractive index of lens is 1.5 and its both the surfaces have same radius of curvature R. The value of R will be _________cm. (where u = object distance, v = image distance)

<p>for point B, &nbsp;<math><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>u</mi></mrow></mfrac><mo>=</mo><mo>−</mo><mn>0</mn><mo>.</mo><mn>1</mn><mn>0</mn><mi>c</mi><msup><mrow><mi>m</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>, </mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>v</mi></mrow></mfrac><mo>=</mo><mn>0</mn></mrow></math></p><p>Thus u = 10 cm, v =&nbsp;<math><mrow><mo>∞</mo></mrow></math></p><p>i.e., f = 10 cm</p><p><math><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>1</mn><mn>0</mn></mrow></mfrac><mo>=</mo><mrow><mo> (</mo><mrow><mn>1</mn><mo>.</mo><mn>5</mn><mo>−</mo><mn>1</mn></mrow><mo>)</mo></mrow><mrow><mo> (</mo><mrow><mfrac><mrow><mn>2</mn></mrow><mrow><mi>R</mi></mrow></mfrac></mrow><mo>)</mo></mrow><mo>⇒</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi>R</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>1</mn><mn>0</mn></mrow></mfrac></mrow></math></p><p>R = 10 cm</p>

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