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A small filament is at the centre of a h...

A small filament is at the centre of a hollow glass of inner and outer radii 8 cm and 9 cm respectively. The refractive index of glass is 1.50. Calculate the position of the image of the filament when viewed from outside the sphere.

Text Solution

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For refraction at the first surface, `mu_(1)=1,mu_(2)=1.50,u=-8 cm`
R = -8cm
`mu_(2)/v-mu_(1)/u=(mu_(2)-mu_(1))/R`
`(1.5)/(v.)-100/(-8cm)=(1.50-1.00)/(-8cm)`
v = -8 cm
It means that due to the first surface the image is formed at the centre of the sphere. For the second surface, `mu_(1)=1.50,mu_(2)=1,u=-9cm,R=-9cm`
`mu_(2)/v-mu_(1)/u=(mu_(2)-mu_(1))/R`
`1/v=1.50/(-9cm)=(1-1.50)/(-8cm)`
v = -9 cm
Hence, the final image is formed at the centre of the sphere.
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