JEE Mains Model Paper 2

The convex lens formula for a real image is

1

v

+

1

u

=

1

f

Where no sign conventions are to be used. Multiplying by u we get

u

v

+1 =

u

f

or

1

m

=

u

f

−1 =

u−f

f

or m(u - f) = f or u =

(1+m)f

m

..... (ii)
Multiplying (i) by v we get
1 +

v

u

=

v

f

or 1 + m =

v

f

or v = f (1 + m) ..... (iii)
Now u + v = d. Using (ii) and (iii) we have
d =

(1+m)f

m

+ f (1 + m)
which gives f =

md

(1+m)2