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

`1.0cm` if the light is incident form the side of concave lens and `2.5mm` if it is incident form the side of the convex lens and the corresponding ratio of intensities are `1//4` and `4`

Explanation

If light is incident form side of convex lens

For fianl light ray to be parallel to the axis of the lens, the image formed by the mirror should be at the focus of the lens.
therefore, the final beam wil be `||` to incident ray.
`(AB)/(CD) = (10)/(5)`
`rArr CD = (AB)/(2) = (AB)/(2) = (5)/(2) mm = 2.5mm`
Power, `P` = constant
`:. I_(1) A_(1) = I_(2) A_(2)`
`rArr (I_(2))/(I_(1)) = (A_(1))/(A_(2)) = (D_(1)^(2))/(D_(2)^(2)) = [(5)/(5//2)]^(2) = 4`
If light is incident form side of concave lens, first image is formed at the focus of concave lens means at the focus fo convex lens. Therefore, final ray will be `||` to incident one.
`(AB)/(CD) = (10)/(5)`
`rArr AB = 2 xx CD = 2xx5 mm`
`(I_(2))/(I_(1)) = (A_(1))/(A_(2)) = (D_(1)^(2))/(D_(2)^(2)) = ((5)/(10))^(2) = (1)/(4)`