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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