Optics Tutorial 6 HW solutions

1.A single refractive surface is used to image an object. The object is 100 mm away and is 7.5 mm tall. The refractive surface has a 100 mm convex radius of curvature and an index of 3.2. Use a YNU ray trace to determine the image location and height. 
– Extra credit: Use the lens makers equations to check image location and similar triangles to check your image height.

Solution: Using the blank spreadsheet provided at the homework page and a solver to find the final image distance, the height is 6.25 mm
 
Spreadsheet below

Thin lens solution: Have to find image distance using:
n'/s' = ((n'-1)/R) + (1/s), solve for s'
s' = n'[((n'-1)/R) + (1/s)]-1 = 3.2[((3.2-1)/100) + (1/{-100})]-1= 3.2[((2.2)/100) - (1/100)]-1= 3.2[(1.2)/100]-1= 3.2*100/1.2 = 266.7mm
The chief ray will refract at the lens. Since the chief ray height at the lens is zero, the surfaces optical power does not come into the equation.
To first order u = n' * u', and we don't need full snell's law. The refracted angle is simply u' = u / n'.
The input chief ray angle = object_height/object_distance or u = h / s
Or u' = h / (s*n')
Finally the object_height = u' * image_distance or
Object_height = h * image_distance / (s * n') = 7.5 * 100 / (266.7 * 3.2)
Image_height = 6.25 mm

Zemax Solution (attached below) shows an image of ~10 and the errors are likely due to the small angle approximation

2.A biconvex singlet is used to visual observe a image. Conduct a YNU ray trace for the eye’s fovea. Assume: 
– Eye has a pupil diameter of 5 mm
– Eye relief of 25 (eye is 25 mm from lens)
– Edmund lens #32624
• Radius of 50.8 mm
• Lens thickness of 5.0 mm
• N-BK7 (index of 1.5168 at 587 nm) Fovea has a 1° half angle (chief ray angle

Solution:

Spreadsheet below
Zemax model below.
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Scott Sparrold,
Mar 7, 2013, 11:25 AM
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Scott Sparrold,
Mar 7, 2013, 1:03 PM
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Scott Sparrold,
Mar 7, 2013, 11:30 AM
Ĉ
Scott Sparrold,
Mar 7, 2013, 1:04 PM
ċ
Problem 1.ZMX
(2k)
Scott Sparrold,
Mar 7, 2013, 1:05 PM
ċ
Problem 2.ZMX
(2k)
Scott Sparrold,
Mar 7, 2013, 1:05 PM
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