A magnifying lens has a focal length of 100mm. An object whose size is 16mm is placed at some distance from the lens so that an image is formed at a distance of 25cm in front of the lens.
- What is the distance between the object and the lens?
- Where should the object be placed if the image is to form at infinity?
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- Given, focal length (f) = 100mm
Image distance (v) = 25 cm = 250mm
Lens formula is given by,
$\frac{1}{\text{f}}=\frac{1}{\text{v}}-\frac{1}{\text{u}}$
$\frac{1}{100}=\frac{1}{250}-\frac{1}{\text{u}}$
$\frac{1}{\text{u}}=\frac{1}{250}-\frac{1}{100}$
$\frac{1}{\text{u}}=\frac{2-5}{500}$
$\frac{1}{\text{u}}=-\frac{3}{500}$
$\text{u}=-166.67\text{mm}$
$\text{u}=-16.66\text{cm}$
The object is at a distance of 16.66 cm and in front of the mirror. The image is at a distance of 25cm and in front of the mirror. Therefore, the distance between the object and the image is 25cm - 16.66cm = 7.14cm.
- The object should be placed at the focus for the image to be formed at infinity.
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