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The distance between two point sources of light is 24cm. Find out where you would place a converging lens of focal length 9 cm, so that the images of both the sources are formed at the same point.

Answer
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Hint: For lens the distance of the image formed from the lens is given by 1v  1u = 1f where u, v and f are a distance of the object, a distance of image, and the focal length respectively.

The focal length is the distance from the center of the lens to the principal foci or the focal points of the lens. For a converging lens, the best example is a convex lens. The focal length is positive and the interval at which a beam of collimated light will be focused on a single spot.

Complete step by step solution:
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S1we have to take the equation as
1v11x=19
Then the equation becomes
1v1+1x=19
Now we want the value of 1v1 so take it outside
1v1=191x.........(1)
Now forS2we have to take the equation as
1v21(24x)=19
Then the equation becomes
1v2+1(24x)=19
Now we want the value of 1v2 so take it outside
1v2=191(24x)
Now Since, the sign convention for S1 and S2is just opposite. Hence, we should take
v1=v2
Then the equation becomes
1v1=1v2
Therefore now substitute the values so we get
191x=124x19
Solving this equation, we get x=6 cm. Therefore, the lens should be kept at a distance of 6 cm from either of the objects.

Note: A converging lens is defined as a lens that converges rays of the light that are moving parallel to the principal axis. The fact that a double convex lens is thicker across its middle is an indicator that it will converge rays of light that move parallel to its principal axis.
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