# An object 4 cm in height, is placed at 15 cm in front of a concave mirror of focal length 10 cm. At what distance from the mirror should a screen be placed to obtain a sharp image of the object. Calculate the height of the image. - Science

An object 4 cm in height, is placed at 15 cm in front of a concave mirror of focal length 10 cm. At what distance from the mirror should a screen be placed to obtain a sharp image of the object. Calculate the height of the image.

#### Solution

Using the mirror equation,

1/v+1/u=1f

⇒1/v+1/(−15)=1/(−10)

⇒1/v=1/(−10)+1/(15)

⇒1/v=(−15+10)/150

1/v=−5/150

v=−30 cm

Thus, to obtain a sharp image of the object the screen should be placed in front of the mirror at a distance of 30 cm from the mirror.
Magnification:

m=−v/u=h_i/h_o

m=−(−30)/(−15)

m=−2

−2=h_i/4

⇒h_i=−8 cm

The image height will be 8 cm.

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