Need to clear confusion on a simple lense problem (solution is worked out )

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In summary, the conversation discusses finding the focal length of a lens with given radii of curvature and indices of refraction. The solution is found using the lensmaker's equation and the sign convention for determining the convexity of the lens surfaces. The focal length is negative because the lens is diverging.
  • #1
Arshad_Physic
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Need to clear confusion on a simple lense problem (solution is worked out :D)

Homework Statement



The following thin lenses are made of glass
of index of refraction 1.7 and are in air with
index of refraction 1.
Find the focal length of a lens with r1 =
22 cm and r2 = 8 cm.

Homework Equations



1/f = (n-1)[(1/R1)-(1/R2)]

The Attempt at a Solution



n of glass = 1.7
n of air = 1

R1 =22 cm

R2 = 8 cm

So, I plug it in the above equation

1/f = (1.7 - 1) (1/22 - 1/8)

f = -17.95918367 cm

I need to clear up few concepts.

1) Is f negative because this lens in Diverging (is it diverging? I was expecting the question to mention it! :D)

2) is my working correct? My answer should be negative? Its kind of wierd! :)

3) How do I figure out from the question as to which side is convex and which side is concave?

Thanks! :)
Arshad
 
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  • #2


Arshad_Physic said:

Homework Statement



The following thin lenses are made of glass
of index of refraction 1.7 and are in air with
index of refraction 1.
Find the focal length of a lens with r1 =
22 cm and r2 = 8 cm.

Homework Equations



1/f = (n-1)[(1/R1)-(1/R2)]

The Attempt at a Solution



n of glass = 1.7
n of air = 1

R1 =22 cm

R2 = 8 cm

So, I plug it in the above equation

1/f = (1.7 - 1) (1/22 - 1/8)

f = -17.95918367 cm

I need to clear up few concepts.

1) Is f negative because this lens in Diverging (is it diverging? I was expecting the question to mention it! :D)

2) is my working correct? My answer should be negative? Its kind of wierd! :)

3) How do I figure out from the question as to which side is convex and which side is concave?

Thanks! :)
Arshad
The sign convention is:
R1 is the radius of curvature of the lens surface closest to the light source,
R2 is the radius of curvature of the lens surface farthest from the light source
R1 is positive if the first surface is convex, and if R1 is negative the first surface is concave. The signs are reversed for the back surface of the lens: if R2 is positive the back surface is concave, and if R2 is negative the back surface is convex.
The focal length f is positive for converging lenses, and negative for diverging lenses.
You can read more here
http://en.wikipedia.org/wiki/Lens_(optics)#Lensmaker.27s_equation
 
  • #3


thanks so much! This really helps!:)
 

1. What is the problem with the lens?

The lens is not focusing properly, resulting in blurry images.

2. What could be causing the issue?

There could be several reasons for the lens not focusing properly, including dirt or smudges on the lens, incorrect camera settings, or a defect in the lens itself.

3. How can I fix the problem?

First, check to see if there are any dirt or smudges on the lens and clean it accordingly. Then, make sure the camera settings are appropriate for the type of photography you are doing. If the issue persists, the lens may need to be repaired or replaced.

4. Can I prevent this problem from happening in the future?

Yes, regularly cleaning and maintaining the lens can help prevent similar issues from occurring. Additionally, double-checking camera settings before taking photos can also prevent focus issues.

5. Should I attempt to fix the lens myself?

It is not recommended to try and fix the lens yourself, as it can be a delicate and complex process. It is best to seek professional help or consult the lens manual for troubleshooting tips.

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