An object 30 cm tall is placed on the principal axis of a convex lens. Its 10 cm tall inverted image is formed on the screen placed at a distance of 15 cm from the lens. Calculate the focal length of the lens.
Answers
Explanation:
lens its 10cm tall inverted image is formed on the screen ... a distance of 15cm from the lens calculate the focal length ...
The focal length of the lens is 11.25 cm.
Given:
Height of object ( O ) = 30 cm
Height of image ( I ) = - 10 cm
Distance of image from the lens (v) = 15 cm
To Find: the focal length of the lens.
Solution:
Let the distance of the object from the lens be 'u'.
We know that the linear magnification formula is;
⇒ m = Height of image ( I ) / Height of object ( O )
= Distance of image (v) / distance of object (u) = v / u
∴ - 10 / 30 = 15 / u
⇒ 10 u = - 450
⇒ u = - 45 cm [ ' - ' shows that object is placed in front of lens ]
Now, using the formula of lens,
1 / f = 1 / v - 1 / u [ where f = focal length of lens ]
= 1/15 - 1 / (- 45 )
= 1/15 + 1/45
= 4/45 cm^-1
∴ f = 45 / 4 cm
= 11.25 cm
Hence, the focal length of the lens is 11.25 cm.
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