September 8th, 2009
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Lens Collimating
Lens Collimating
Single Slit Diffraction?


A collimated beam of mercury green light 546.1nm is normally incident on a slit 0.015cm wide. A lens of focal length 60cm is placed behind the slit. A diffraction pattern is formed on a screen placed in the focal plane of the lens. Determine the distance between
(i) the central maximum and first minimum and
(ii) the first and second minima. Use radians
Could someone please give me a solution for this! Seriously desperate!

The assumption is reluctantly made (see ref.) that the ray angles from slits to screen are not changed by the lens, and that the lens is immediately next to the slit, thus the diffraction angle equations are unaffected by presence of the lens.
1. m = 1
Θ1 = arcsin(m*lambda/d) = 3.64067470922265E-03 rad
2. m = 2
Θ2 = arcsin(m*lambda/d) = 7.28139767493248E-03 rad
Distance = Θ2-Θ1 = 3.64072296570983E-03 rad



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To get the best images from your telescope, its optics must be in precise alignment. This economical tool will ensure that they are. It's a combination sight tube and Cheshire eyepiece, consisting of a 5"-long tube made of black-anodized aluminum. It fits in a 1.25" eyepiece holder. A peephole in the top and wire crosshairs at the bottom enable precise centering of Newtonian optical components. The polished 45-deg internal surface projects an annulus of light into the optical path to facilitate primary mirror alignment. Simply insert the Collimating Eyepiece in the focuser drawtube and follow normal collimation steps. Your Newtonian will always be in excellent optical alignment! Instructions included.

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Determine the ABCD matrix for a beam translated a distance d1, focused through a thin lens for focal lenght f1


a) Determine the ABCD matrix for a beam translated a distance d1, focused through a thin lens for focal lenght f1, and then translated a distance d2.
b) A collimated beam (plan waves) arrives at a concave mirror with a focal length of 0.15 m and is then focused by the mirror. Write out the ABCD matrix for this process

a)Let
MT(d)={{1,d},{0,1}}
MF(f)={1,0},{-1/f,1}}
Then the matrix you want is

M=MT(d2). MF(f).MT(d1)={{A,B},{C,D}}
={{1 - d2/f, d1 + d2 - (d1 d2)/f}, {-(1/f), 1 - d1/f}}

b)The question should state more clearly what the input and output planes are. If I assume the first to be at the mirror and the second at its focal point, then, with f=.15 m:
M=MT(f).MF(f)={{0, f}, {-(1/f), 1}}={{0., 0.15}, {-6.66667, 1.}}

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