A point object O is placed on the axis of a cylindrical piece of glass of refractive index 1.6 as shown in the figure. One surface of the glass piece is convex with radius of curvature 3mm. The point appeared to be at 5 mm on the axis when viewed along the axis and from right side of convex surface. The distance of the point object from the convex surface is :

Options

A. 4 mm
B. 6 mm
C. 3 mm
D. 2.5 mm

Answer

A

Explanation

A point object O is placed on the axis of a cylindrical glass as shown in the figure,

For a curved spherical surface,
`(mu_(2))/(v)+(mu_(1))/(u)=(mu_(1)-mu_(2))/(R)`
where, `v=5`mm, `R=-3` mm, `mu_(1)=1.6` and `mu_(2)=1`
Putting the given values in the above expression,
we get
`1/5+(1.6)/(u)=(1.6-1)/(-3)`
`(1.6)/(u)=-0.2-1/5=-2/5`
`rArr u=-(1.6xx5)/(2)=-4`mm
Hence, the correct option is (a).