 All right friends so this is a quick video wherein we will be talking about the equivalent focal length right now most of us know how to find the equivalent focal length if multiple thin lenses are placed in contact let us say this is one of the lens this is the second lens and this is third lens right so the equivalent focal length formula for the case where let's say f1 f2 f3 these three focal lengths lenses they are in contact then the equivalent focal length formula we know is 1 by f1 plus 1 by f2 plus 1 by f3 is equal to 1 by f right so there is no confusion here we can substitute the value of focal length these focal length will be positive for converging lenses and will be negative for the negative for the diverging lenses okay now there will be certain situations where the lens and the mirrors are placed in combination okay so again let us take a simple scenario wherein one of the convex lens the other side is silver okay so here what will happen to a ray let's say there is a ray that goes in straight like this converging lens will converge it right then what will happen the mirror on the other end of the lens that will also try to reflect so that it converges backwards right and while it is going through the lens it will further converge right so you can see that the lens is converging two times wherein the mirror is converging the ray only once now I'm all simplifying things here so that you can remember the formula okay so this is the path of the ray that is parallel to the principal axis now wherever it hits the distance of the at from optical center is my equivalent focal length right now if I try to find out this value of the focal length by using proper method so let us try to find out that way first okay so first it will pass to the lens let's say focal length let's say focal length of the lens is f and let us say the focal length of the mirror is f m okay let me take it as f l and f m okay now when the ray is hitting the lens I can use the lens formula 1 by v minus 1 by u equal to 1 by f right so the first image let's say v1 minus u is infinity and it is encountering the lens of focal length f l so this is my first equation okay now what will happen it will hit the mirror right when it hits the mirror I will have to use the mirror formula 1 by v plus 1 by u equal to 1 by f this formula I have to use okay now the image of the lens v1 is the object of the mirror okay so I can write it as 1 by v2 plus u is v1 and f is focal length of the mirror okay this is my second equation now the ray is traveling backwards to the lens okay now when it is traveling backwards to the lens our sign convention reverses right because while it is going towards the right instant ray we were taking this side negative and that side positive but when it is traveling in the reverse direction and I'm taking the lens for the second time this side is positive that side is negative okay so since sign convention is reversed and if I have to use the lens formula for the second time 1 by v1 sorry 1 by v where v is the image which is the final image that would be equal to 1 by f let us say okay and u should be ideally equal to the image of the mirror but since sign convention is reversed I will be writing it as minus u2 okay this is equal to 1 by f l so this is my third equation okay so you can see here that if you subtract the second equation from the first equation okay you will get minus 1 by v2 is equal to 1 by f l minus 1 by f n right then when I add these three and four equations I will get 1 by f is equal to 1 by f l plus 1 by f l minus 1 by f n okay so this will give me 2 by f l minus 1 by f m okay now one thing you need to understand here that this focal length that you have in the third equation this focal length is as per the sign convention which is reversed fine so you are getting this focal length by having a reverse sign convention okay so based on your original sign convention if you have to find the focal length you have to take negative of this okay so I'll write it as 1 by f dash because it is by using the reverse sign convention so 1 by f should be equal to minus or 1 by f dash so 1 by f is equal to minus 2 by f l plus 1 by f m okay so you can see in this case you will have to use that formula wherein 1 by f is equal to minus 2 by f l plus 1 by f m okay now this focal length of mirror you when you substitute the value of course it will be a negative quantity okay and length focal length in this case will be a positive quantity okay so the idea is that if let us say multiple lenses are placed side by side and let's say at the end there is a lens so 1 by focal length of the equivalent combination is equal to minus 2 by focal length of the first lens first lens minus 2 by focal length of the second lens and so on plus 1 by focal length of the mirror okay so you can probably remember the formula something like this wherein you can see the effect of the lens this parallel ray when it hits the lens it converges okay it tries to converge forward but because the mirror the overall convergence happens to be backwards so the effect of the mirror is reversed because of the presence of the lenses so that is why when we are talking about the lens there is a negative sign over there fine so let me summarize it by using one of the examples here this is one of the lens this is the other lens and let us say at the end I have a concave lens and the end of the concave lens is still over so let us say this is the scenario okay first lens let's say has a focal length of f1 second has f2 third lens has let us say f3 and the mirror over here has the focal length of fm okay so 1 by f equivalent of these three combination will be equal to minus 2 by f1 minus 2 by f2 minus 2 by f3 and plus 1 by fm okay so I hope this is very easy to remember all you have to do is in this equivalent focal length formula you have to use a sine dimension to get the correct answer okay all right now many a times we are in a hurry and we generally assume that the focal length of the mirror which is because it is formed on the lens would be equal to focal length of the lens okay that is not at all correct fine if let us say focal length of the lens is given we need to use the lens maker formula here guys mu minus 1 1 by r1 minus 1 by r2 and let us say if it is an equi convex or equi concave lens find out the radii of curvature if let us say 1 by fl sorry find out the radii of curvature from the focal length of the lens and let us say this side radius of curvature is r1 then focal length of the mirror would be equal to r1 by 2 okay so the relation for the focal length of the mirror with the radius of curvature is straightforward but for lens you have to first find out the radius of curvature in order to determine the focal length of the mirror that is made out of the lens okay so I hope all of this is clear to you you can get in touch with me and get your doubts clarified in case there are any