Ray Optics and Optical Instruments Part 2

Given, focal length of first lens, f1=+10‌cm
Focal length of second lens, f2=−10‌cm
Focal length of third lens, f3=+30‌cm
Object distance from first lens, u1=−30‌cm
Using lens formula for first lens, we get

1

f1

=

1

v1

−

1

u1

⇒

1

−10

=

1

v1

−

1

−30

⇒

1

v1

=

1

10

−

1

30

=

2

30

v1=15‌cm
Thus, the image formed by first lens is 15 cm to the right of first lens.
The object distance for second lens will be
u2=15‌cm−5‌cm=10‌cm
Using lens formula for first lens, we get

1

f2

=

1

v2

−

1

u2

⇒

1

−10

=

1

v2

−

1

10

⇒

1

v2

=

1

−10

+

1

10

=0
⇒v2=∞
Thus, the object distance for third lens, u3 = ∞.
Using lens formula for third lens, we get

1

f3

=

1

v3

−

1

u3

⇒

1

30

=

1

v3

−

1

∞

1

v3

=

1

30

v3=30‌cm
The final image will form 30 cm from the third lens.
The distance of final image from object will be 30+10+5+30=75‌cm
Thus, the distance of final image formed from object O is 75 cm.