Because the formula can't distinguish otherwise between right and left, as you primarily using only magnitude of lengths in the derivation through similar triangles. The sign convention I have applied is: $\beta_1=+1$ when left surface is convex $\beta_1=-1$ when left surface is concave $\beta_2=+1$ when right surface is concave The mirror equation \(\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\) holds good for concave mirrors as well as convex mirrors. Why don't we use sign convention during the derivation of a lens maker formula? Mirror Thin Lens . the effect of signs of that variable cancells. If you want to see what I am saying, try deriving the lens formula, using these two conditions. Here is the lenses makers equation write explicitly with the sign conversion terms, $$ Sign convention is a set of rules to set signs for image distance, object distance, focal length, etc for mathematical analysis of image formation. Sign Convention for Spherical Mirrors and Thin Lenses Applies to: Mirror and Thin Lens Equation: 1/ d o + 1/ d i = 1/ f Magnification Equation: Image height/Object height = h i / h o = - d i / d o ... second mirror/lens. Refer to the diagram for clear visualization. But for the third, RESULT, you only applaying convention once that at the time of derivations and that remains there which ensure that the answer is in the same convention. When image is formed in front of the mirror, the distance of image is taken as – (negative) and when image is formed behind the mirror, the … Why do internal forces not affect the conservation of momentum, Understanding the mechanics of a satyr's Mirthful Leaps trait, Importance of “gerade” to express “just about to”. We get-, Since, \(\frac{1}{v}+\frac{1}{u}=\frac{1}{f}\) we can re- arrange it as –, On substituting the values in the above equation we get-. To calculate the Focal length of the given mirror, substitute the value of Radius of Curvature (R) in the \(f=\frac{R}{2}\). The distance between the object and the pole of the mirror is called the object distance(u). What do these left arrows or angle brackets mean to the left of a chord? Since, the centre of curvature and focus lie in front of the concave mirror, so signs of radius of curvature and focal length are taken as negative in the case of concave mirror. According to it: Object is always placed to the left of mirror; All distances are measured from the pole of the mirror. Have any other US presidents used that tiny table? Meaning of the Term "Heavy Metals" in CofA? Derivation of lens formula or mirror equation; Sign Conventions. Since, object is always placed in front of the mirror hence the sign of object is taken as negative. Why does my voltage (reduced with a voltage divider) drop to zero when connected to a 6V DC motor? This way you can ignore the sign of the lens radius and simply set the sign terms ($\beta_1$ and $\beta_2$) to correct values for the particular type of lens you are studying. (1) image on right and object on left of lens. BTW, do you know why you use sign convention in the first place ? According to me we should ,as the mirror/lens formula is for an individual apparatus,and cannot be for the whole problem. (2) image on left and object on left. The radius of curvature of a convex mirror used for rearview on a car is 4.00 m. If the location of the bus is 6 meters from this mirror, find the position of the image formed. Required fields are marked *, Mirror Equation for concave mirror and Mirror Equation for a convex mirror. I have just started learning optics at school and my teacher derived the lens and mirror formulas. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. f is the Focal Length given by \(f=\frac{R}{2}\), R is the radius of curvature of the spherical mirror. At the time of derivation you applaying the signs for U,V,F thar guarantee that U,V,F are in our convention. This general lens formula is what you were after which you can use in other special scenarios by applying the sign convention. $$. rev 2020.11.24.38066, The best answers are voted up and rise to the top, Physics Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, Sign convention for mirror and lens formulas, “Question closed” notifications experiment results and graduation, MAINTENANCE WARNING: Possible downtime early morning Dec 2/4/9 UTC (8:30PM…. The image is 1.5 meters behind the mirror. Also, do you know a virtual image is kind of an optical illusion only, as to there is nothing there behind the mirror. Should we leave technical astronomy questions to Astronomy SE? \frac{1}{f} = \left(n-1\right)\left( \frac{d\left(n-1\right)}{\beta_1\beta_2n\bigl|R_1\bigr|\bigl|R_2\bigr|} + \frac{\beta_1}{\bigl|R_1\bigr|} - \frac{\beta_2}{\bigl|R_2\bigr|} \right) The sign convention I have applied is: $\beta_1=+1$ when left surface is convex $\beta_1=-1$ when left surface is concave $\beta_2=+1$ when right surface is concave Its kind of like applying sign convention gives a particular formula and applying it twice cancels the effect of the sign convention at all,giving you the general lens formula. If you want to calculate radii to give fixed focal length then having the equation in this form makes rearranging for the required terms very simple. $-----$ What is the meaning of 肩にこてん in " 俺の肩にこてんと頭を預けて". Can we change the sign convention (distance measured in the direction of incident ray positive and opposite negative) midway solving a problem. This way you can ignore the sign of the lens radius and simply set the sign terms ($\beta_1$ and $\beta_2$) to correct values for the particular type of lens you are studying.
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