Question

The distance between two points sources of light is 24cm where should a convergent lens with a focal length of f=9 be placed between them to obtain the image of both source at the same point?​

Answer 1

Answer:

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Answer 2

Answer:

Given: distance between two point sources of light, d=24cm, convergent lens focal length, f=9cm

To find the position at which the lens should be placed so that the image obtained of both sources is at same point

Solution:

Let the distance between first object and lens be x

The the distance between second object and lens will be 24−x

And the sign convention of image of second object will be negative.

Then, according to lens formula

for first object

1/f =1/v +1/u

⟹ 1/9=1/v +1/x.......(i)

and for the second object

1/9 = 1/ (-v) + 1 / (24-x)........(ii)

now adding equation (i) &(ii)

1/9 +1/9 = 1/v + 1/x - 1/v + 1/ (24-x)

⟹ 2/9 = 1/x + 1/ (24-x)

⟹ 2/9 = (24-x+x) / [ x(24-x)]

⟹2/9 = 24 / (24x - x²)

⟹ 2(24x - x²) = 24×9

divide throughout by 2, we get

x² −24x+108=0

⟹x(x−18)−6(x−18)=0

⟹(x−6)(x−18)=0

⟹x=6,x=18

Hence the lens can be placed at 6cm or 18 cm from the first source in order to get both sources image at same distance.

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