# Plano-concave thin lens, checking my result

Gold Member

## Homework Statement

Determine the focal length of a plano-concave lens (n=1.5) which has a radius of curvature of 10 cm. What is its power in diopters?

None given.

## The Attempt at a Solution

1/f=(n-1)(1/R_1-1/R_2)=(1/2)(-0.1)=-1/20.
Thus f=5 cm and P=-20 m^(-1).
Is this right?

## Answers and Replies

Staff Emeritus
Homework Helper
Hi,

Your method is mostly correct, but you have made some arithmetic errors.

## Homework Equations

None given.
Really? Because ...

## The Attempt at a Solution

1/f=(n-1)(1/R_1-1/R_2)
... this looks like an equation to me =(1/2)(-0.1)=-1/20.
Pretty much correct. R2 is considered negative, so -1/R2 would be +1/(20cm).
(Edit: this is wrong, R2 is positive. See my next post.)
Thus f=5 cm and P=-20 m^(-1).
Is this right?
Not quite. You went from 1/f = 1/20 (←correct) to f = 5 Try that last bit of algebra again, you are very close.

RB

Last edited:
Gold Member
Hi,

Your method is mostly correct, but you have made some arithmetic errors.

Really? Because ...

... this looks like an equation to me I'm not given any tip about what equation to use, therefore I thought I might confuse someone willing to help me if I put a wrong equation in the "relevant equations". But from now on, I must use this section as an attempt to relevant equations. Pretty much correct. R2 is considered negative, so -1/R2 would be +1/(20cm).

Not quite. You went from 1/f = 1/20 (←correct) to f = 5 Try that last bit of algebra again, you are very close.

RB

From my sketch R_1=infinity and R_2>0. Should I reach 1/f=-1/20?
Ok for the rest, f=20 or -20 depending on my question.
Any ray of light has to pass by the plane part and then the concave part according to my sketch. I'm sure I should reach 1/f=20, but I do not reach this. Should I recheck my calculations? I have (n-1)(-1/R_2) and as R_2>0, I get a negative result. Strange.
Thanks for the help.

Staff Emeritus
Homework Helper
From my sketch R_1=infinity and R_2>0. Should I reach 1/f=-1/20?
You're absolutely correct. For some reason, I read the question as saying "plano-convex". My mistake.

Ok for the rest, f=20 or -20 depending on my question.
It's -20, you were correct about it being negative. Of course, there should be units included when you report the answer.

Gold Member
You're absolutely correct. For some reason, I read the question as saying "plano-convex". My mistake.

It's -20, you were correct about it being negative. Of course, there should be units included when you report the answer.

There's no problem. Thanks for the correction, your time and your help.
As for the units, I think the ones in my first posts are OK.

Staff Emeritus
I get it, thanks. 