Respuesta :
Answer:
The final image be located 2 cm behind the second lens.
(a) is correct option.
Explanation:
Given that,
Focal length = +2 cm,
Object distance = 4 cm
If a second identical lens is now placed 8 cm behind the first
We need to calculate the image distance
Using formula of focal length
[tex]\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}[/tex]
Put the value into the formula
[tex]\dfrac{1}{2}=\dfrac{1}{v}+\dfrac{1}{-4}[/tex]
[tex]\dfrac{1}{v}=\dfrac{1}{2}+\dfrac{1}{4}[/tex]
[tex]\dfrac{1}{v}=\dfrac{3}{4}[/tex]
[tex]v=1.333\ cm[/tex]
Where two lens are separated by 8 cm
The image of first lens become object for second lens
Then object distance is
[tex]u = 8 -1.33= 6.67 cm[/tex]
Where two lens are same means have same focal length then image distance is
Using formula of lenses
[tex]\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}[/tex]
Put the value into the formula
[tex]\dfrac{1}{2}=\dfrac{1}{v}+\dfrac{1}{-6.67}[/tex]
[tex]\dfrac{1}{v}=\dfrac{1}{2}+\dfrac{1}{6.67}[/tex]
[tex]v=1.54\ cm[/tex]
Round off value of v is 2 cm
Hence, The final image be located 2 cm behind the second lens.
