Question

A point object is placed on the principal axis of a convex lens (f = 15 cm) at a distance of 30 cm from it. A glass plate (μ = 1.50) of thickness 1 cm is placed on the other side of the lens perpendicular to the axis. Locate the image of the point object.

Answer 1

Given,
Convex lens of focal length (f) = 15 cm
Object distance, (u) = −30 cm
Using lens formula,
$$\begin{gathered} \frac{1}{v}-\frac{1}{u}=\frac{1}{f} \\ \Rightarrow \frac{1}{v}=\frac{1}{f}+\frac{1}{u} \\ \Rightarrow \frac{1}{v}=\frac{1}{15}-\frac{1}{30}=\frac{1}{30} \\ \Rightarrow v=30 \end{gathered}$$

Thus ,v = 30 cm
Therefore, the image of the object will be formed at a distance of 30 cm to the right side of the lens.
[since, μ_g = 1.5 and thickness (t) = 1 cm]

$\mathrm{\Delta }t=\left(1-{\displaystyle \frac{1}{{\mathrm{\mu }}_{\mathrm{g}}}}\right)t$
$=1-\frac{2}{3}=\frac{1}{3}=0.33\mathrm{cm}$
Hence, the image of the object will be formed at 30 + 0.33 = 30.33 cm from the lens on the right side, due to the glass having thickness 1 cm.