# Finding lens information

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1. Apr 14, 2015

### AaronBurr

1. The problem statement, all variables and given/known data
I've tried to attached the image of the diagram. If that isnt working please let me know.

Height of incident marginal ray now 25. Assume a thin lens.
Find:
a. the effective focal length
b. the power of the lens
c. surface curvature for front and back surfaces (assume equiconvex shape)
d. radius of curvature for each surface
e. format size (assume square)
f. Airy disk diameter

2. Relevant equations
a. the effective focal length
1/f=1/u+1/v
F=1/2*r

b. the power of the lens
p=1/f

c. surface curvature for front and back surfaces (assume equiconvex shape)
C=1/R

d. radius of curvature for each surface
F=1/2*r

e. format size(assume square)

f. Airy disk diameter
=2.44*λ*f ⁄#

3. The attempt at a solution
With the known formulas I dont think I have enough information to solve anything besides f. and the solution to part f doesn't help solve the other parts. If I can just find the focal length I think the rest will fall into place.Can you point me towards whatever bit of information I'm missing?

Thanks so much.

#### Attached Files:

• ###### Lesson 1 Homework-lens design.3.pdf
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2. Apr 15, 2015

### andrevdh

The f-number is the ration of the focal length to the diameter of the entrance pupil.

3. Apr 15, 2015

### AaronBurr

Thank you so much! I knew I was just missing something obvious! I think I've got parts a, b, c, d, and f correct. But I'm still a bit unsure of what is being asked in part e? I dont know what they mean by format size. Any ideas? Again thank you for your help.

a. the effective focal length

F-number=f/d
1/10=f/25mm
F=5/2

b. the power of the lens

p=1/f
p=1/(5/2)
p=2/5

c. surface curvature for front and back surfaces (assume equiconvex shape) (Both lens have same radius of curvature)

C1=1/R
C1=1/5

d. radius of curvature for each surface

f=1/2*r
R1=2*f
R=2*(5/2)
R=5

e. format size(assume square)

??

f. Airy disk diameter

=2.44*λ*f⁄#
=2.44*587nm*1/10
=143.228

4. Apr 16, 2015

### andrevdh

F = f / D
10 = f / 50 mm ....
The optical power of the lens, P, is in diopters, D, if f is in meters.
The surface curvature of a lens, C, also in diopters, is much more complicated than that of a mirror.
It is the inverse of the radius of curvature, r, in meters, of the lens.
Have a look in your textbook or notes for the formula.