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A sunshine recorder globe of 30 cm diame...

A sunshine recorder globe of `30 cm` diameter is made of glass of `mu = 1.5`. A ray enters the globe parallel to its axis. Find the position from the centre of the sphere, where the ray crosses the axis.

Text Solution

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For first refraction at surface `AP_(1)`
`u = oo, v = P_(1)I_(1) = ?`
`R = + 15 cm, mu_(2) = 1.5, mu_(1) = 1`
`-(mu_(1))/(u) +(mu_(2))/(V) = (mu_(2) - mu_(1))/(R )`
`-(1)/(oo) + (1.5)/(v) = (1.5 - 1)/(15) = (1)/(30), v = 45 cm`.
The image would have been formed at `I_(1)` if glass medium were continuous.

For second refraction at surface `BP_(2)`
`I_(2)` acts as virtual object.
`u = P_(2)I_(1) = P_(1)I_(1) - P_(1)I_(2) = 45 - 30 = 15 xm`
`R = -15 cm, v = P_(2)I = ?`
`-(mu_(2))/(u) + (mu_(1))/(v) = (mu_(1) - mu_(2))/(R )`
`(1.5)/(15) + (1)/(v) = (1 - 1.5)/(-15) = (1)/(30)`
`(1)/(v) = (1)/(30) + (1)/(10) = (4)/(30)`
`v = (30)/(4) = 7.5 cm`
Distance of image `I` from the centre of sphere
`CI = CP_(2) + P_(2)I = 15 + 7.5 = 22.5 cm`
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