Question

a) A candle is placed at 90 cm apart from a screen. Where
should a convex lens of focal length 20 cm be placed in between candle
and the screen so that a real and diminished image of the candle is
formed distinctly on the screen?​

Answer 1

Explanation:

only example plzz follow me

Answer 2

Answer:

A convex lens with a focal length of $20 cm$ should be positioned between the candle and the screen, forming a real and decreased image of the candle on the screen at $\mathrm{f}=21.4 \mathrm{~cm}$

Explanation:

For two-positions of convex lens, the image of the object can be located on the screen, with u and v swapped.

The separation between two positions of the lens is, $d=20 \mathrm{~cm}$

From the figure,

$\mathrm{u}_{1}+\mathrm{v}_{1}=90 \mathrm{~cm}$

$\mathrm{v}_{1}-\mathrm{u}_{1}=20 \mathrm{~cm}$

Solving,

$\mathrm{v}_{1}=55 \mathrm{~cm}, \mathrm{u}_{1}=35 \mathrm{~cm}$

From lens formula,

$\begin{aligned}&\frac{1}{\mathrm{v}}-\frac{1}{\mathrm{u}}=\frac{1}{\mathrm{f}} \\&\frac{1}{55}-\frac{1}{-35}=\frac{1}{\mathrm{f}}\end{aligned}$

$\begin{aligned}&\Rightarrow \frac{1}{\mathrm{f}}=\frac{1}{55}+\frac{1}{35}=\frac{55 \times 35}{90} \\&\Rightarrow \mathrm{f}=21.4 \mathrm{~cm}\end{aligned}$