At what position a candle of length 3 cm be placed in front of a convex lens so that it's image of length 6 cm be obtained on a screen placed at distance 30 cm behind the lens
Height of object=3cm
Height of image=-6cm (formed below principle axis )
V=30 cm
U=?
By using lens formula we get f=10cm
hi/ho=v/u
-6/3=30/u
U=-15 cm
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To determine the position where the candle should be placed in front of a convex lens, we can use the lens formula:
1/f = 1/v - 1/u,
where:
- f is the focal length of the lens,
- v is the image distance from the lens,
- u is the object distance from the lens (position of the candle).
In this case, we know:
- Length of the object (candle) = 3 cm,
- Length of the image = 6 cm,
- Distance of the screen from the lens (v) = 30 cm.
To find the image distance (v), we can use the magnification formula:
magnification (m) = -v/u,
where:
- magnification (m) = image size / object size.
Given the image size (6 cm) and object size (3 cm), we can substitute these values into the magnification formula:
m = (6 cm) / (3 cm).
Since we know that the magnification (m) is negative for a real and upright image, we have:
-2 = -v/u.
Substituting the focal length (f) of the lens into the lens formula, we have:
1/f = 1/v - 1/u.
Simplifying the lens formula, we get:
1/f = (-1/u) - (1/u) = -2/u.
Rearranging the equation, we can express u (object distance) in terms of f:
1/f = -2/u,
u = -2f.
Using the relation:
u + v = 30 cm,
we can substitute u = -2f to find v:
-2f + v = 30 cm,
v = 30 cm + 2f.
Now, we need to substitute the values into the relation:
m = -v/u.
-2 = -(30 cm + 2f) / (-2f).
Simplifying this equation, we can find the value of f. Once we have the value of f, we can substitute it in the equation v = 30 cm + 2f to find the value of v. Finally, we can determine the position of the object (candle) by subtracting u from the lens to screen distance (v).