Question

A lens suffers from spherical aberration. Its diameter is 200mm and it has focal lengths of 990 mm for rays incident at the edge of the lens and 1000 mm for rays 50 mm away from the optic axis.
(i) What is the position of the plane which contains the circle of least confusion?
(ii) What is the size of the image in this plane?

Answer 1

Answer on Question 54963, Physics / Astronomy | Astrophysics

(i) By similar triangles:

$$\frac {D}{F _ {i}} = \frac {S}{x}, \text{ and } \frac {d}{F _ {o}} = \frac {S}{F _ {o} - (F _ {i} + x)}$$

Eliminating S, we have:

$$\frac {d}{F _ {o}} = \frac {D x}{F _ {i} \times [ F _ {o} - (F _ {i} + x) ]}$$

Rearranging we have:

$$x = \frac {d F _ {i} \times (F _ {o} - F _ {i})}{D F _ {o} + d F _ {i}} = \frac {100 \times 990 \times (1000 - 990)}{(200 \times 1000) + (100 \times 900)} = 3.3 \text{ mm}$$

Answer: $x = 3.3 \text{ mm}$

(ii) Now:

$$s = \frac {x D}{F} = \frac {3.3 \times 200}{990} = 0.67 \text{ mm}$$

Answer: $s = 0.67 \text{ mm}$

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