COMBINATION OF LENSES


QUESTIONS: Two convex lenses of focal length f_{1} and f_{2} 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 "p_{1}" from the lenses L_{1} whose real image I_{1} is formed at a distance q_{1}. 

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 L_{2}
will be the same as its distance from L_{1}. If L_{2} forms
an image I_{2} of this virtual object at a distance q_{2} then p_{2}. _{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"f_{1}" and "f_{2}" by a single lens of focal length "f" such that it forms an image at a distance q_{2} of an object placed at a distance p_{1} 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
f_{1}>f_{2} the combined lens behaves as a concave lens. If f_{2}> f_{1} 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} 
