Question

A convex lens of focal length 20 cm and a concave lens of focal length 10 cm are placed 10 cm apart with their principal axes coinciding. A beam of light travelling parallel to the principal axis and having a beam diameter 5.0 mm, is incident on the combination. Show that the emergent beam is parallel to the incident one. Find the beam diameter of the emergent beam.

Answer 1

Hello mate!!




Let, the parallel beam is first incident onconvex 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, the emergent beam becomes parallel after refraction in concave lens.
As shown from the triangles XYB and PQB,

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.


HOPE IT HELPS YOU

Answer 2

Given :

convex lens f=20cm

concave lens focal length =f= -10cm

distance between both lens= 10cm

Beam diameter = 5mm

According to question;

beam of parallel lines are incident on convex lens  

For concave lens:

u= +10cm [as it is virtual object ]

f=10cm

Lens formula:

1/v-1/u=1/f

1/v=-1/10+1/10 =infinity

=∞

v= infinity

Thus after refraction in the concave lens, emergent beam becomes parallel

ΔXYB and ΔPQB

PQ/ Xy=RB/ZB=10/20=1/2

PQ=1/2 x 5=2.5mm

∴Beam diameter is 2.5mm