|
|
COMBINATION OF LENSES
|
||
| QUESTIONS: Two convex lenses of focal length f1 and f2 are in contact with each other. Find their equivalent focal length. |
||
| ANSWER: | ||
| consider
two convex lenses in contact such that their separation is very small as
compared to their focal length. Let a point object "O" is placed at a distance "p1" from the lenses L1 whose real image I1 is formed at a distance q1. |
||
 |
||
|
Using
thin lens formula
|
||
 .........(1) |
||
| Image
servers as a virtual object for the second lens. If we neglect small distance
between the lenses ,the distance of this virtual object from lens L2
will be the same as its distance from L1. If L2 forms
an image I2 of this virtual object at a distance q2 then p2. For latest information , free computer courses and high impact notes visit : www.citycollegiate.com |
||
 |
||
 ........(2) |
||
| Adding equation (1) and equation (2) | ||
   |
||
| now if we replace the two lenses of focal lengths"f1" and "f2" by a single lens of focal length "f" such that it forms an image at a distance q2 of an object placed at a distance p1 from it as shown such lens is called equivalent lens and | ||
 |
||
| Its focal length is known as equivalent focal length. For the above lens | ||
 |
||
|
www.citycollegiate.com
|
||
| comparing equation (3) and equation (4) , we get | ||
|
||
| If
f1>f2 the combined lens behaves as a concave lens. If f2> f1 the combined lens behaved as a convex lens. Note : above two conditions are valid if one lens is convex and the other is concave lens . If both lenses are convex then the combined lens will behave like a convex lens. For latest information , free computer courses and high impact notes visit : www.citycollegiate.com |
||