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 $3\, mm$. 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:

• 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, $v=5 \,m , R=-3 \,mm , \mu_{1}=1.6$ and $\mu_{2}=1$
Putting the given values in the above expression, we get
$\frac{1}{5}+\frac{1.6}{u}=\frac{1.6-1}{-3}$
$\frac{1.6}{u}=-0.2-\frac{1}{5}=-\frac{2}{5}$
$\Rightarrow \, u=-\frac{1.6 \times 5}{2}=-4 \,mm$