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A spherical glass flask of radius R = 60 mm is completely filled with water (refractive index 4/3). It acts as a lens and forms an inverted image of a distant object. Find the distance d1 (in cm) from the centre of the flask to the centre of the image.

1. 6
2. 12
3. 18
4. 24

Correct answer: 12

Solution

Two refractions at spherical surfaces. R = 6 cm. First surface (object at infinity, light enters water sphere): n1=1, n2=4/3, R1=-6 cm (center of curvature on the same side as incident ray). (n2-n1)/R1 = n2/v1 - n1/u1 => (1/3)/(-6) = (4/3)/v1 => v1 = -24 cm (virtual image inside sphere, 24 cm from first surface, or 24-12=12 cm beyond second surface). Second surface: object at u2 = +12 cm (virtual object), n1=4/3, n2=1, R2=-6 cm. (1 - 4/3)/(-6) = 1/v2 - (4/3)/12 => (1/3)/6 = 1/v2 - 1/9 => 1/v2 = 1/18 + 2/18 = 1/6 => v2 = 6 cm beyond exit surface. Distance from centre = 6 + 6 = 12 cm.

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