Geometrical Optics

The magnification is expressed as m =

f

f+u

Therefore,

m25

m50

=

f+u50

f+u25

=

20−50

20−25

=

−30

−5

= 6
Alternative Solution: Using the lens formula,

1

v

+

1

u

=

1

f

, for the two positions of the object gives

1

v1

−

1

−25

=

1

20

;

1

v2

−

1

−50

=

1

20

.
From the first equation, we get v1 = 100 cm and the second equation gives v2 = 100/3 cm. Hence, the magnification is thefirst case is m25 = v

1

u1

= - 4 and that in the second case is m50 =

v2

u2

= −

2

3

. Hence ,

m25

m50

= 6.