Physics - Geometrical Optics Question with Solution | TestHub

Let a large convex lens is placed between two walls at a distance$x$from the wall on which an electric bulb is fixed.

Using

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

$=\frac{1}{4-x}-\frac{1}{-x} \left(\because u=-x, v=4-x\right)$

$=\frac{x+4-x}{\left(4-x\right)\left(x\right)}$

$=\frac{4}{(4-x)\left(x\right)}$

$or f=\frac{\left(4-x\right)x}{4} \dots \dots \left(i\right)$

Now magnification$m=\frac{v}{u}=\frac{4-x}{x}$

$⟹ 1=\frac{4-x}{x}$

$⟹x=4-x$

$⟹2x=4$

$⟹x=2 \mathrm{m}$

From eq. (i)

$f=\frac{(4-2)\left(2\right)}{4}=\frac{2\times 2}{4}=1 \mathrm{m}$