Question

A pencil, 4.0cm in size, is placed at-25.0cm in front of a concave mirror
of focal length 15.0cm. At what distance from the mirror should a screen
be placed in order to obtain a sharp image? Find the nature and the size
of the image.​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

height of the image (hi) = 4 cm

object distance (u) = -25 cm

focal length (f) = -15 cm

using mirror formula,

$\frac{1}{f} =\frac{1}{u} +\frac{1}{v}$

$\frac{1}{-15} =\frac{1}{-25} +\frac{1}{v}$

$\frac{1}{v} =\frac{1}{25} -\frac{1}{15}$

$\frac{1}{v} =\frac{6 - 10}{150}$

v= 150/-4

v= -37.5 cm.

Nature of the image = real and inverted

size of the image ,

using ,magnification formula ,

$m=\frac{hi}{ho} =\frac{-v}{u}$                           [ for mirrors]

so m = -37.5/25

    m = -3/2 = -1.5

so hi/ho = -1.5

    hi = -1.5*4

    hi = -6 cm                         [negative because it is below the principal axis]

so, size of the image = 6 cm ,which is magnified.

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