A concave mirror with a focal length of 43 cm produces an image whose distance from the mirror is one-fifth the object distance. Find the object and image distances.
Object: __________ cm
Image: __________ cm
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1/f = 1/v + 1/u
Hence, 1/43 = 5/u + 1/u
Hence, u=43x6 cm = 258 cm
image distance = v = u/5 = 258/5 = 51.6 cm
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A concave mirror with a focal length of 37 cm produces an image whose distance from themirror is one-half the object distance. Find the objectand image distances.
object | cm |
image | cm |
answer
Given
focal length f = 37 cm
image whose distance from the mirror isone-half the object distance
image distance v = u /2
--------------------------------------------------------------
( 1 / f) = ( 1 / u ) +(1/ v)
( 1/f ) = (1/ u) + ( 2 / u)
u = 3f
object distance u = 111cm
image distance v = 55.5cm
The formula that relates focal length (f), object distance (o) and image distance (i) is
1/f = 1/o + 1/i
or f =o*i/o+i
since the distance of the image is half that of the object distance
it can be written as i = o/5 or o= 5*i.
Expressing o in terms of i and substituting in the equation for f,
we get
f = 5*i*i/5i+i
f =5i/6
since f is given as 43 cm
i = 43*5/6 = 35.83 cm
o = 5*35.83 = 179.15 cm
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