Question

A convex lens of focal length 20cm and a concave lens of focal length 10cm are placed in contact in such a way that they have the common principal axis. What will be the nature of the lens so formed and the focal length of this combination? plz fast

Answer 1

Explanation:

Let, the parallel beam is first incident on convex lens.

d = diameter of the beam = 5 mm

Now, the image due to the convex lens should be formed on its focus (point B)

So, for the concave lens,

u = +10 cm (since, the virtual object is on the right of concave lens)

f = 10 cm

So ,

v

1

−

u

1

=

f

1

⇒

v

1

=

−10

1

+

10

1

=0⇒v=∞

So, the emergent beam becomes parallel after redfraction in concave lens.

As shown from the triangles XYB and PQB,

XY

PQ

=

ZB

RB

=

20

10

=

2

1

PQ=

2

1

×5=2.5 cm=25mm

So, the beam diameter becomes 2.5 mm.

Similarly, it can be proved that if the light is incident of the concave side, the beam diameter will be 1cm.