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

A, B, C, D

Explanation

Let the parallel beam is first incident on convex lens.
d=diameter of the beam =5mm
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=-10cm`
`So, 1/v-1/u=1/f`
`rarr 1/v=1/(-10)+1/(+10)=0`
`rarrv=0`
So, the emergent beam becomes parallel after refraction in concave lens.
As shown from the triangle XYB and
`PQ=1/2xx5=2.5mm`
(PQ)/(XY)=(RB)/(ZB)=10/20=1/2`
So, the beam diameter becomes 2.5 mm. Similarly it can proved that if the light is incident of the concave side, the beam diameter will be 1 cm.