Question

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 $5mm$ 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:

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

Answer 1

Answer: (A)

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

For a curved spherical surface,
$\frac{{\mu }_2}{v}+\frac{{\mu }_1}{u}=\frac{{\mu }_1-{\mu }_2}{R}$
where, $v=5m,R=-3mm,{\mu }_1=1.6$ and ${\mu }_2=1$
Putting the given values in the above expression, we get
$\frac{1}{5}+\frac{1.6}{u}=\frac{1.6-1}{-3}$
$\frac{1.6}{u}=-0.2-\frac{1}{5}=-\frac{2}{5}$
$\Rightarrow u=-\frac{1.6\times 5}{2}=-4mm$