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Answers
Here is your answer
first case ,focal length=30cm
second case ,when the object is moved 20cm towards the lens , the image will be formed at 60cm
Magnification is negative so this implies that the image is real and inverted.
Also magnification is 1 this means that the image and object are of the same size.
This is possible only if the object is kept at the centre of curvature.
So in this case image distance = object distance.
u = v = 60/2 = 30cm
u = -30cm and v = 30cm
Focal length is r/ 2
R = - 30cm so focal length is 15cm
It is a convex lens.
If object is moved 20 cm towards lens then u = -10cm
We know that
1/f = 1/v - 1/u (lens formula)
1/f + 1/u = 1/v
1/15 + -1/10 = 1/v
2-3/30 = 1/v
-1/30 = 1/v
v = - 30cm
m = v/u = -30/-10 = +3
So the image is going to be virtual as magnification is positive and object is kept between focus and optic centre.