Question

|1l|
M. An object is placed in front of two convex lenses
one by one at a distance u from the lens. The focal
lengths of the lenses are 30 cm and 15 cm
respectively. If the size of image formed in the two
cases is same, then u is
(1) 15 cm
(2) 20 cm
(3) 25 cm
(4) 30 cm​

Answer 1

Answer: We know , magnification given by lens is

m=f/f+u

Note: If u is distance then we will put '−u' in the formula as formula demands co−ordinates and not distances

F1=30cm

f2=15cm

m1=30/30−u

m2=15?15−u

Since size of image in two cases are same

⇒m1=m2 or m1=−m2

(both image might be real in that case magnifications are equal. Or if one is real and one is virtual then magnification of one is minus times the other)

Now

m1=m2

30/30−u=15/15−u

2/30−u=1/15−u

30−2u=30−u

u=0

But u cannot be zero

For

m1=−m2

30/30−u=−15/15−u

2/30−u=1/u−15

2u−30=30−u

3u=60

u=20cm