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A converging lens of focal length 0.18 m is used to produce an image of an object on a screen. If a magnification of 9.0 x is required, calculate the distance from the object at which the screen must be placed.

Respuesta :

Answer:

distance between object and screen is 2 m

Explanation:

given data

focal length = 0.18 m

magnification = 9.0 x

to find out

distance from the object

solution

we know that magnification is express as

magnification m = [tex]\frac{v}{u}[/tex]   .............1

here u is distance of object from lens

and v is distance of image from lens

so here

9 = [tex]\frac{v}{u}[/tex]

v = 9 u   ..................2

now we will apply here lens formula that is

[tex]\frac{1}{f} = \frac{1}{u} + \frac{1}{v}[/tex]        ....................3

put here value f is focal length and v = 9 u

[tex]\frac{1}{0.18} = \frac{1}{u} + \frac{1}{9u}[/tex]  

solve it we get

u = 0.2

so v = 9 (0.2 )

v = 1.8

so here distance between object and screen is v +u

distance between object and screen = 1.8 + 0.2

distance between object and screen is 2 m

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