Answer:
The focal length of the lens is 5.54 cm and the height of the image is -0.89 cm.
Explanation:
Given that,
Height of object h = 2 cm
Object distance u= -18 cm
Image distance v= 8 cm
We need to calculate the focal length of the lens
Using formula of lens
[tex]\dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u}[/tex]
Where, f = focal length
Put the value into the formula
[tex]\dfrac{1}{f}=\dfrac{1}{8}-\dfrac{1}{-18}[/tex]
[tex]\dfrac{1}{f}=\dfrac{13}{72}[/tex]
[tex]f=5.54\ cm[/tex]
(II). We need to calculate the height of the image
Using formula of magnification
[tex]m =\dfrac{v}{u}=\dfrac{h'}{h}[/tex]
[tex]\dfrac{v}{u}=\dfrac{h'}{h}[/tex]
Put the value into the formula
[tex]\dfrac{8}{-18}=\dfrac{h'}{2}[/tex]
[tex]h'=\dfrac{8}{-18}\times2[/tex]
[tex]h'=-0.89\ cm[/tex]
Hence, The focal length of the lens is 5.54 cm and the height of the image is -0.89 cm.
