An object is kept at a distance of 100m from a screen. A convex lens has to be placed in between such that an image is formed on the screen and image size is four times the object size. Find the focal length .
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Explanation:
The distance between object and screen, i.e., (u + v) = 100 cm
Magnification, m = -4 (negative due to real image)
To Find:
The focal length of lens.
Calculation:
- As (u+v) = 100
⇒ v = 100 - u
- Magnification = v / u
⇒ m = (100-u) / u
⇒ -4 = (100/u) -1
⇒ u = - 100/3 cm
- Again, using the formula for magnification:
m = f / (f + u)
⇒ mf + mu = f
⇒ f = mu / (1-m)
⇒ f = {-4 × (-100/3)} / {1-(-4)}
⇒ f = (400/3) × 1/5
⇒ f = 80/3 cm
or f = 26.67 cm
- So, the focal length of lens is 26.67 cm.
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