
The distance between two point sources of light is 24cm. Find out where you would place a converging lens of focal length , so that the images of both the sources are formed at the same point.
Answer
484.5k+ views
Hint: For lens the distance of the image formed from the lens is given by where and 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:
we have to take the equation as
Then the equation becomes
Now we want the value of so take it outside
Now for we have to take the equation as
Then the equation becomes
Now we want the value of so take it outside
Now Since, the sign convention for and is just opposite. Hence, we should take
Then the equation becomes
Therefore now substitute the values so we get
Solving this equation, we get . Therefore, the lens should be kept at a distance of 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.
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:

Then the equation becomes
Now we want the value of
Now for
Then the equation becomes
Now we want the value of
Now Since, the sign convention for
Then the equation becomes
Therefore now substitute the values so we get
Solving this equation, we get
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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