At what distance should an object be placed from a lens of focal length 25 cm to obtain its image on the screen?

Given,

The focal length of a convex lens, f =  18 cm.

Image distance, v = 24 cm

Object distance, u = ?

To find- Magnification

Solution:

By using lens formula-

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}\phantom{\rule{0ex}{0ex}}$

where, v = image distance, u = object distance, and f = focal length

Substituting the values of f, v and u we get,

$\frac{1}{24}-\frac{1}{u}=\frac{1}{18}\phantom{\rule{0ex}{0ex}}$

$\frac{1}{24}-\frac{1}{18}=\frac{1}{u}\phantom{\rule{0ex}{0ex}}$

$\frac{18-24}{24\times 18}=\frac{1}{u}\phantom{\rule{0ex}{0ex}}$

$\frac{6}{24\times 18}=\frac{1}{u}\phantom{\rule{0ex}{0ex}}$

$\frac{1}{4\times 18}=\frac{1}{u}\phantom{\rule{0ex}{0ex}}$

$u=-72cm\phantom{\rule{0ex}{0ex}}$

So, the object distance is -72cm.

The object should be placed at a distance of -72 cm from the lens.

Now, the equation for finding magnification of a lens can be given as-

$m=\frac{v}{u}\phantom{\rule{0ex}{0ex}}$

Substituting the values in magnification formula we get-

$m=\frac{24}{-72}\phantom{\rule{0ex}{0ex}}$

$m=-\frac{1}{3}\phantom{\rule{0ex}{0ex}}$

Hence, the magnification produced will be $m=-\frac{1}{3}\phantom{\rule{0ex}{0ex}}$

At what distance should an object be placed from a lens of focal length 25 cm to obtain its image on a screen placed on the other side at a distance of 50 cm from the lens? What will be the magnification produced in this case?

Given that,

Focal length, f = 25 cm

Image distance, v = 50 cm

Form the lens formula,

`1/v-1/u=1/f`            (where u = object distance)

`"or", 1/u=1/v-1/f`

`=1/50-1/25`

Therefore,

`1/u=(-1)/50`

Or, u = −50 cm

Magnification, `m=v/u`

`=50/(-50)`

= -1

The object must be placed 50 cm away from the lens, on the other side to produce a magnification of −1.

Concept: Magnification Due to Spherical Lenses

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