A linear object of length 4 cm is placed at from the plane surface of hemispherical glass of radius 10 cm. The hemispherical glass is surrounded by water. Find the final position and size of the image.

Explanation

For Ist surface,
`mu_(1)=4/3,mu_(2)=3/2,u=-20cm and R=+10 cm`
Using, `mu_(2)/v-mu_(1)/mu=((mu_(2)-mu_(1)))/R`
`rArr ((3//2))/v-((4//3))/((-20))=((3//2-4//3))/10rArrv=-30 cm`
Using, `(A'B')/(AB)=(mu_(1)v)/(mu_(2)u)rArr(A'B')/((4 cm))=((4//3)(-30))/((3//2)(-20))`
`rArr A'B'=5.3cm`
A' B' behaves as the object for plane surface,
`mu_(1)=3/2,mu_(2)=4/3 and R=oo,u'=-40`
`rArrmu_(1)/v'=mu_(2)/u'rArr((4//3))/v'=((3//2))/((-40))`
Solving it, we will get, v'=-35.4 cm
Now, using `(A"B")/(A'B')=((mu_(1)v'))/((mu_(2)u'))`
`(A"B")/((5.3))=((3//2)(-35.4))/((4//3)(-40))`
`rArr`A"B"=5.3 cm
The final images in all the above cases are shown in the figure.