A converging lens of focal length `10cm` and a diverging lens of focal length `5cm` are placed `5cm` apart with their principle axes coinciding. A beam of light travelling parallel to the incident one. Find the beam diameter of the emergent beam is parallel to the incident one. Find the beam diamter of the emergent beam. Alos find out the ratio fo emergent and incident intensities.

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)`