Two convex lenses each of focal length 10 cm, are placed at a separation of 15 cm with their principal axes coinciding. (a) Show that a light beam coming parallel to the principal axis diverges as it comes out of the lens system. (b) Find the location of the virtual image formed by the lens system of an object placed far away. (c ) Find the focal length of the equivalent lens.

Answer

A, B, C, D

Explanation

(a) The beam will diverge after coming out of convex lens system because, the image formed by the first lens lies wtihin the focal length of the second lens. (b) For `I^(st)` Convex les,
`(1)/(upsilon) = (1)/(f) + (1)/(u)`
`=(1)/(10) + (1)/((-oo)) = (1)/(10)`
'[since, mu = -oo]`
or V = 10 cm
For `2^(nd)` convex lens,
`(1)/(upsilon_1) = (1)/(f) + (1)/(u)`
or `(1)/(upsilon_1) = (1)/(10) + (1)/(-(15 - 10))`
`=(1)/(10)+(1)/((-5))`
`= (1)/(10)`
`upsilon = -10 cm`
So, the virtual image will be at 5 cm from `1^(st)` convex lens. (c ) If F be the fonal length of equivalent lens.
Then, `(1)/(F) = (1)/(f_1) + (1)/(f_2) - (d)/(f_1f_2)`
`=(1)/(10 )+ (1)/(10) - (15)/(100)`
`=(1)/(5) - (3)/(20)`
`= (1)/(20)`
or F =20 cm