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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.

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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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