The following matrix product is used in discussing a thick lens in air: A = 1 n − 1 / R 2 0 1 1 0 d / n 1 1 − n − 1 / R 1 0 1 , where d is the thickness of the lens, n is its index of refraction, and R 1 and R 2 are the radii of curvature of the lens surfaces. It can be shown that element A 12 of A is − 1 / f where f is the focal length of the lens. Evaluate A and detA (which should equal 1) and find 1 / f . [See Am. J. Phys. 48, 397 − 399 1980 . ]
The following matrix product is used in discussing a thick lens in air: A = 1 n − 1 / R 2 0 1 1 0 d / n 1 1 − n − 1 / R 1 0 1 , where d is the thickness of the lens, n is its index of refraction, and R 1 and R 2 are the radii of curvature of the lens surfaces. It can be shown that element A 12 of A is − 1 / f where f is the focal length of the lens. Evaluate A and detA (which should equal 1) and find 1 / f . [See Am. J. Phys. 48, 397 − 399 1980 . ]
The following matrix product is used in discussing a thick lens in air:
A
=
1
n
−
1
/
R
2
0
1
1
0
d
/
n
1
1
−
n
−
1
/
R
1
0
1
,
where d is the thickness of the lens, n is its index of refraction, and
R
1
and
R
2
are the radii of curvature of the lens surfaces. It can be shown that element
A
12
of A is
−
1
/
f
where f is the focal length of the lens. Evaluate A and detA (which should equal 1) and find
1
/
f
.
[See Am. J. Phys. 48,
397
−
399
1980
.
]
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