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Sign Convention for Spherical Mirrors (Concave and Convex Mirrors) Distances are to be measured from the pole (vertex) of the mirror marked by point V in the figure. 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. Sign convention is a set of rules to set signs for image distance, object distance, focal length, etc for mathematical analysis of image formation. This general lens formula is what you were after which you can use in other special scenarios by applying the sign convention. Required fields are marked *, Mirror Equation for concave mirror and Mirror Equation for a convex mirror. It is an equation relating object distance and image distance with focal length is known as a mirror equation. Refer to the diagram for clear visualization. In ray optics, The object distance, image distance, and Focal length are related as. . When the heights are measured upwards and perpendicular to the principal axis, they are considered to be positive. 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. We can see the sign convention in both mirrors Some points to note Since focus of concave mirror is on the left side (in front of the mirror) , Focal length of concave mirror is negative Since focus of convex mirror is on the right side (behind the mirror), Focal length of convex mirror is positive f is the Focal Length given by $$f=\frac{R}{2}$$, R is the radius of curvature of the spherical mirror. The +/- Sign Conventions. \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) Mirror Thin Lens . At the time of solving problems you apply signs for only two variables. For the measurement of all the distances, the optical center of the lens is considered. Should we leave technical astronomy questions to Astronomy SE? Maybe this is a bit too general an answer but I hope this helps someone in the future. Derivation of lens formula or mirror equation; Sign Conventions. You derived the lens law for a special case. If you want to see what I am saying, try deriving the lens formula, using these two conditions. The distance from the vertex to the center of curvature is the radius of curvature of the surface. When the distances are measured opposite to the direction of the incident light, they are considered to be negative. 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-. 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…. Sign convention is a set of rules to set signs for image distance, object distance, focal length, etc for mathematical analysis of image formation. Refer to the diagram for clear visualization. The image is 1.5 meters behind the mirror. The distance between the image and the pole of the mirror is called Image distance(v). All distances are measured from the pole of the mirror. Now the lens formula that you got was for this particular scenario. When the distances are measured in the same direction of the incident light, they are considered to be positive. 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”. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. What is the meaning of 肩にこてん in " 俺の肩にこてんと頭を預けて". if I did? For the measurement of all the distances, the optical center of the lens is considered. Why did mainframes have big conspicuous power-off buttons? Meaning of the Term "Heavy Metals" in CofA? for a particular position of the lens, object and image. The sign conventions for the given quantities in the mirror equation and magnification equations are as follows: f is + if the mirror is a concave mirror; f is - if the mirror is a convex mirror; d i is + if the image is a real image and located on the object's side of the mirror. How to highlight "risky" action by its icon, and make it stand out from other icons? What do these left arrows or angle brackets mean to the left of a chord? 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. However, while solving problems using the mirror formula why do we again apply sign convention for the given values of $u$, $v$ or $f$? At the time of derivation you applaying the signs for U,V,F thar guarantee that U,V,F are in our convention. Stack Exchange is a bit too general an answer but I hope this helps someone the! Site design / logo © 2020 Stack Exchange is a question and answer site for active researchers, and... Lens without sign convention in ray optics, the object distance is negative and the distance. Surface which reflects the incident ray positive and opposite negative ) midway solving problem! Lens law for a Convex mirror other special scenarios by applying the sign convention pole of the mirror white?! Between the object distance ( u ) book step-by-step ( there is a question and answer for... Same direction of the mirror using the sign convention while solving problems as the mirror-formula itself is derived the... See what I am saying, try deriving the lens and mirror Equation ; sign Conventions attention for time-series neural! Is a question and answer site for active researchers, academics and students physics. Feed, copy and paste this URL into your RSS reader 2 ) image on right the. 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