Question

a spherical concave mirror has a radius of curvature 6 CM at what distance from the mirror should a 6 CM object be placed to obtain an image that is 48 CM tall​

Answer 1

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Answer 2

Given that,

Radius of curvature of concave mirror, R = 6 cm

Size of the object, h = 6 cm

Size of image, h' = 48 cm

To find,

Object distance from the mirror

Solution,

Focal length of the mirror is, f = R/2 = 6/2 = -3 cm (negative form concave)

Magnification is given by :

$m=\dfrac{-v}{u}=\dfrac{h'}{h}\\\\\dfrac{48}{6}=\dfrac{-v}{u}\\\\\dfrac{-v}{u}=8\\\\v=-8u\ .........(1)$

Now using mirror's formula as :

$\dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}\\\\\dfrac{1}{(-8u)}+\dfrac{1}{u}=\dfrac{1}{-3}\\\\u=-2.62\ cm$

So, the object is placed at a distance of 2.62 cm from the mirror.

Learn more,

Mirror's formula

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