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An object is at a distance of d=2.5 cm f...

An object is at a distance of `d=2.5 cm` from the surface of a glass sphere with a radius `R=10 cm.` Find the position of the final image produced by the sphere. The refractive index of glass is `mu_ = 1.5.`

Text Solution

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As the mark is on one surface, refraction will take place on the other surface (which is curved). Further refraction is taking place from glass to air. So,
`mu_(1)=1.5 , mu_(2)=1,R=-5cm, u=-10cm,v=?`
Using the formula
`mu_(2)/v mu_(1)/u=(mu_(2)-mu_(1))/R`,We have
`1/v - 1.5/((-10)=(1-1.5)/(-5)`or v=-20cm
Hence, the image is at a distance of 20 cm from P towards O.
In case of refraction at a curved surface, we have
`m=1/O = mu_(1)/mu_(2) v/u =((1.5)xx(-20))/(1xx(-10))=+3`So, the image is virtual, erect and of size
`I= m xx O = 3 xx 0.2 = 0.6 cm = 6 mm`
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