Respuesta :
Answer:
Focal length of the lens is 8.2 cm.
Explanation:
It is given that,
Height of object, h = 4 cm
Object distance, u = -30 cm
Height of the image, h' = -1.5 cm (negative because the image is inverted)
We need to find the focal length of the lens. It can be calculated using lens formula as :
[tex]\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}[/tex]
Magnification, [tex]m=\dfrac{v}{u}=\dfrac{h'}{h}[/tex]
[tex]\dfrac{v}{-30}=\dfrac{-1.5}{4}[/tex]
Image distance, v = 11.25 cm
[tex]\dfrac{1}{11.25}-\dfrac{1}{-30}=\dfrac{1}{f}[/tex]
f = 8.18 cm
or f = 8.2 cm
So, the focal length of the lens is 8.2 cm. Hence, this is the required solution.
The focal length of the object with height 4.0 cm is distance between the middle of lens to the focal point. The focal length of the lens is 8.2 cm.
What is focal length of the lens?
The focal length of the lens is length of the distance between the middle of the lens to the focal point.
It can be find out using the following formula as,
[tex]\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}[/tex]
Here, (v)is the distance of the image, (u) is the distance of the object, and (f) is the focal length of the lens.
Given information-
The height of the object is 4.0 cm.
The distance between the object and the lens is 30 cm.
The height of the image is 1.5 cm.
As the ratio of distance of image to the distance of the object is equal to the ratio of height of the image to the height of the object.
Suppose the distance of the image is [tex]v[/tex]. Thus,
[tex]\dfrac{v}{-30}=\dfrac{-1.5}{4}\\v=11.25\rm cm[/tex]
Hence, the distance of the image is 11.25 cm.
Put the values in the lens formula as,
[tex]\dfrac{1}{11.25}-\dfrac{1}{-30}=\dfrac{1}{f}\\f\cong8.2\rm cm[/tex]
Hence, the focal length of the lens is 8.2 cm. Thus the option D is the correct option.
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