A concave lens of focal length 20 cm produces a image of 1/4 time magnified. Find the object distance?
Answers
m=ff+u
12=−20−20+u or −20+u=−40
or u=−40+20 or u=−20cm.
Answer:
The object's distance from the given concave lens is found to be 60 cm.
Explanation:
We are given that the lens produces an image times magnified, thus, we can say that the magnification of the lens provided is or 0.25.
Now, we know that the magnification of any lens is found by the following expression:
where 'm' is the magnification, 'u' is the distance of the object from the lens and 'v' is the distance of the image from the lens.
Now, after substituting the magnification and cross multiplying, we get:
...(i)
Now, we know the focal length of the given lens.
Whether the lens is concave or convex, it is found to be following the lens equation which is given below:
Now, substituting the value of focal length and eq.(i) in this, we get:
Taking LCM and solving, we get:
After cross multiplication, it becomes:
cm
Now, substituting 'v' in (i), we get:
u = 60 cm
Thus, the object's distance from the lens is found to be 60 cm.
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