Answer:
The focal length of the lens is -5.88 cm.
Explanation:
We know that magnification in case of lenses is given by
[tex]m=\frac{v}{u}[/tex]
where
'v' is the position of image
'u' is the position of the object
Since it is given that m = 0.4 thus we can write
[tex]\frac{v}{u}=0.4\\\\\therefore v=0.4u[/tex]
Now the distance between the object and the image in case of concave lens is given by
[tex]u-v =5.3\\\\u-0.4u=5.3\\\\\therefore u=\frac{5.3}{(1-0.4)}=8.84cm\\\\v=0.4\times 8.84=3.54cm[/tex]
Now by lens formula the focal length of the lens is given by
[tex]\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\\\\\frac{1}{f}=\frac{1}{-3.54}-\frac{1}{-8.84}\\\\\therefore f=-5.88cm[/tex]
