A screen is placed a distance 40 cm away from an illuminated obje… - Vidyadip

MCQ

A screen is placed a distance $40\ cm$ away from an illuminated object. A converging lens is placed between the source and the screen and it is attempted to form the image of the source on the screen. If no position could be found, the focal length of the lens:

A
Must be less than $10\ cm.$
✓
Must be greater than $20\ cm.$
C
Must not be greater than $20\ cm.$
D
Must not be less than $10\ cm.$

✓

Answer

Correct option: B.

Must be greater than $20\ cm.$

$\text{v}=(40-4)$
$\frac{1}{\text{f}}=\frac{1}{40-4}-\frac{1}{(-\text{u})}$
$\frac{\text{df}}{\text{du}}=0$ for f minimum.
$\frac{\text{df}}{\text{du}}=1-\frac{\text{u}}{20}=0$
$\text{u}=20$
$\text{f}_{\text{min}}=10\text{cm}$

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