A transparent sphere of radius R has a cavity of radius R2 as shown in figure. The refractive index of the sphere is μ=a+bc. If a parallel beam of light falling on left surface focuses at point P, find the value of [bc – a]

μv=μ−1R v=μRμ−1 U'=v−R=Rμ−1 1R−μR(μ−1)=2(1−μ)R μ2−3μ+1=0 μ=3+52

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A transparent sphere of radius R has a cavity of radius $\frac{R}{2}$ as shown in figure. The refractive index of the sphere is $μ = \frac{a + \sqrt{b}}{c}$ . If a parallel beam of light falling on left surface focuses at point P, find the value of [bc – a]

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Detailed Solution

$\frac{μ}{v} = \frac{μ - 1}{R} v = \frac{μ R}{μ - 1} U^{'} = v - R = \frac{R}{μ - 1} \frac{1}{R} - \frac{μ}{R} (μ - 1) = \frac{2 (1 - μ)}{R} μ^{2} - 3 μ + 1 = 0 μ = \frac{3 + \sqrt{5}}{2}$

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