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A solid glass sphere of refractive index mu is struck by a narrow, parallel beam of light aimed at one end of a diameter. Find the value of mu so that the light is brought to focus at the diametrically opposite point C on the sphere's surface.

1. 1
2. 2
3. 3
4. 4

Correct answer: 2

Solution

Let sphere radius = R. First surface (n1=1, n2=mu, R=+R, u=infinity): mu/v = (mu-1)/R => v = mu*R/(mu-1). For light to focus at C (second surface, distance 2R from first): v = 2R => mu*R/(mu-1) = 2R => mu = 2*(mu-1) => mu = 2. At mu=2, the intermediate image falls exactly at the second surface, so the rays converge to C after the second refraction.

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