Question

calculate the focal lenght of lens which has to be contact with convex lens of focal length of 30 cm to produce a lens of focal length 10 cm​

Answer 1

Explanation:

An object is placed 30 cm in front of convex lens of focal length 10 cm :

Given : u

1

=−30 cm f

1

=10 cm

From lens formula,

v

1

1

−

u

1

1

=

f

1

1

∴

v

1

1

−

−30

1

=

10

1

⟹v=15 cm

Thus image is formed at a distance of 15 cm behind the lens.

Now a concave lens of focal length f

2

is placed in contact with convex lens. so the screen has to be shifted by 45 cm further away.

Now the new image distance v

2

=15+45=60 cm

Let the focal length of combination of lens be F.

Using lens formula,

v

2

1

−

u

1

1

=

F

1

∴

60

1

−

−30

1

=

F

1

⟹F=20 cm

Focal length of combination of lenses

F

1

=

f

1

1

+

f

2

1

∴

20

1

=

10

1

+

f

2

1

⟹f

2

=−20 cm (minus sign comes as the focal length of concave lens is negative)