One end of a horizontal cylindrical glass rod `(mu=1.5)` of radius 5.0 cm is rounded in the shape of a hemisphere. Asnobject 0.5 mm high is placed perpendicular to the axis of the rod at a difference of 20.0 cm from the rounded edge. Locate the image of the object and find its height.

Explanation

Refraction at spherical surface,
`mu_1=1.0,mu_2=(3)/(2),mu=-20cm,R=5cm,v=?`
`(mu_2)/(v)-(mu_1)/(u)=(mu_2-mu_1)/(R)`
`((3)/(2))/(v)-(1)/(-20)=((3)/(2)-1)/(5)`
`(3)/(2v)+(1)/(20)=(1)/(10)`
`(3)/(2v)=(1)/(10)-(1)/(20)=(1)/(20)impliesv=30cm`
v is `+ve` i.e., image is formed right of P.
`m=(I)/(O)=(mu_1v)/(mu_2u)`
`(I)/(0.5)=(1xx30)/((3)/(2)xx(-20))impliesI=-0.5mm`
`I` is `-ve` i.e., image is inverted.