The distance between two point sources of light is 24 cm where should you place a
converging lens of focal length 9cm, so that the images of both sources are formed at the
same point?
Answers
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
f
1
=
v
1
+
u
1
⟹
9
1
=
v
1
+
x
1
....(i)
And for second object,
9
1
=
−v
1
+
24−x
1
....(ii)
Adding eqn (i) and (ii), we get
9
1
+
9
1
=
v
1
+
x
1
+
24−x
1
−
v
1
⟹
9
2
=
x
1
+
24−x
1
⟹
9
2
=
x(24−x)
24−x+x
⟹2x(24−x)=9(24)
⟹48x−2x
2
=216
⟹2x
2
−48x+216=0
divide throughout by 2, we get
x
2
−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.