# Is focal length of plano-concave lens $f=\cfrac{R}{\mu - 1}$ or $f=\cfrac{R}{1 - \mu}$?

Let the radius of curvature of the concave part of the lens be $$R$$. Then when using the lens makers equation, $$\cfrac{1}{f} = \left(\cfrac{\mu_2}{\mu_1} - 1\right)\left(\cfrac{1}{R_1} - \cfrac{1}{R_2}\right)$$ $$R_2$$ is clearly $$\infty$$ but is $$R_1 = -R$$ (as convention would assume, since the focal point is ont the left) or is $$R_1 = R$$.

• You can assume two cases when the planar face is on the left, and the one where it is on the right. Both will give the same answer, given you follow the sign conventions. Feb 27, 2019 at 15:13

That depend how you place, the lens and your sign convention let say we have this lens , Let you have surface ET draw a circle containing ET part taking CT as a line passes through origin, you can see it is on left hand side of origin, hence you can take $$R_1=(-)$$, as $$R_2$$ is infinite.
R1 is the Radius of curvature of first surface and R2 of the second. Keeping Plane side as first surface $$\frac{1}{R1}$$=0 while R2=-R. Keeping Concave side as first surface , $$\frac{1}{R2}$$=0 while R1=+R. Where R is radius of curvature of concave part.
• This isn't a yes or no question- they are asking if $R_1=R$ or $-R$.