Question

In a lens displacement method, the distance between the object and screen is $70\text{cm}$, and the focal length of the lens is $16\text{cm}$. Find the separation between the sharp image positions of the lens.

• A. $20.4\text{cm}$
• B. $30\text{cm}$
• C. $17.2\text{cm}$
• D. $42.2\text{cm}$

Answer 1

The correct option is A $20.4\text{cm}$

Given, the distance between the object and screen, $D=70\text{cm}$,
focal length, $f=16\text{cm}$.

$\Rightarrow 4f=64\text{cm}$

$\therefore D>4f$

Hence, there are two positions where a sharp image is formed.

Formula of distance between magnified and sharp image,

$d=\sqrt{D^2-4fD}$

Substituting the values of $f$ and $D$, we have

$d=\pm \sqrt{{70}^2-4\times 16\times 70}$

$\therefore d=\pm \sqrt{420}=\pm 20.4\text{cm}$

Hence the correct answer is option $\left(a\right)$.