9. The following matrix product is used in discussing a thick lens in air: = (₁ (n-1)/R₂) - 1)/R²) (d/n 1) (1 - (n-1)/R¹), A = where d is the thickness of the lens, n is its index of refraction, and R₁ and R₂ are the radii of curvature of the lens surfaces. It can be shown that element A12 of A is -1/f where f is the focal length of the lens. Evaluate A and det A (which should equal 1) and find 1/f. [See Am. J. Phys. 48, 397-399 (1980).]
9. The following matrix product is used in discussing a thick lens in air: = (₁ (n-1)/R₂) - 1)/R²) (d/n 1) (1 - (n-1)/R¹), A = where d is the thickness of the lens, n is its index of refraction, and R₁ and R₂ are the radii of curvature of the lens surfaces. It can be shown that element A12 of A is -1/f where f is the focal length of the lens. Evaluate A and det A (which should equal 1) and find 1/f. [See Am. J. Phys. 48, 397-399 (1980).]
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![9.
The following matrix product is used in discussing a thick lens in air:
(n-1)/R₂)
= (₁
- 1)/R²) (d/n 1) (1 - (n-1)/R¹₁),
A =
where d is the thickness of the lens, n is its index of refraction, and R₁ and R₂ are
the radii of curvature of the lens surfaces. It can be shown that element A12 of A is
-1/f where f is the focal length of the lens. Evaluate A and det A (which should
equal 1) and find 1/f. [See Am. J. Phys. 48, 397-399 (1980).]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa4b86813-5baa-4b0a-a247-9ca8d00e632e%2F5fcf715b-260f-400b-82c4-5043b90dbc02%2Fzwxk2lh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:9.
The following matrix product is used in discussing a thick lens in air:
(n-1)/R₂)
= (₁
- 1)/R²) (d/n 1) (1 - (n-1)/R¹₁),
A =
where d is the thickness of the lens, n is its index of refraction, and R₁ and R₂ are
the radii of curvature of the lens surfaces. It can be shown that element A12 of A is
-1/f where f is the focal length of the lens. Evaluate A and det A (which should
equal 1) and find 1/f. [See Am. J. Phys. 48, 397-399 (1980).]
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