Plano-concave thin lens, checking my result

In summary, the focal length of the plano-concave lens (n=1.5) with a radius of curvature of 10 cm is -20 cm and its power is -20 m^-1. The relevant equations used were 1/f=(n-1)(1/R_1-1/R_2) and R_1=infinity, R_2>0.
  • #1
fluidistic
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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?


Homework Equations



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?
 
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  • #2
Hi,

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

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 :smile:
=(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 :confused:

Try that last bit of algebra again, you are very close.

RB
 
Last edited:
  • #3
Redbelly98 said:
Hi,

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

Really? Because ...... this looks like an equation to me :smile:
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. :smile:

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 :confused:

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.
 
  • #4
fluidistic said:
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.
 
  • #5
Redbelly98 said:
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.
 
  • #6
Yes, your first post had correct units but wrong values for f and P.
 
  • #7
Redbelly98 said:
Yes, your first post had correct units but wrong values for f and P.

I get it, thanks. :smile:
 

1. What is a plano-concave thin lens?

A plano-concave thin lens is a type of lens that has one flat side and one curved side that is concave, meaning it curves inward like a bowl. This type of lens is often used to correct nearsightedness, as it diverges light rays and helps to focus them properly on the retina.

2. How do I check my result when using a plano-concave thin lens?

To check your result when using a plano-concave thin lens, you can use the thin lens equation: 1/f = 1/do + 1/di, where f is the focal length of the lens, do is the distance from the object to the lens, and di is the distance from the lens to the image. You can also use a ray diagram to visualize how the light rays are being refracted by the lens.

3. What factors can affect the accuracy of my result when using a plano-concave thin lens?

The accuracy of your result when using a plano-concave thin lens can be affected by several factors, including the curvature of the lens, the refractive index of the material the lens is made of, and the accuracy of your measurements for the distances do and di.

4. Can a plano-concave thin lens be used for anything other than correcting nearsightedness?

Yes, a plano-concave thin lens can be used for other purposes, such as in telescopes and microscopes. When used in these instruments, the lens helps to magnify the image by diverging the light rays and making them appear larger.

5. How can I determine the power of a plano-concave thin lens?

The power of a plano-concave thin lens can be determined by calculating the reciprocal of its focal length, which is measured in meters. For example, a lens with a focal length of 0.5 meters would have a power of 1/0.5 = 2 diopters. The higher the power, the more the lens will diverge light rays.

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