Introduction to Geometrical Optics: Sample problems ...€¦ · Introduction to Geometrical Optics:...
Transcript of Introduction to Geometrical Optics: Sample problems ...€¦ · Introduction to Geometrical Optics:...
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Introduction to Geometrical Optics:
Sample problems solutions supplementary slides
Apratim Majumder
Optics for Energy 2020
2020/10/13
-
Fish (Wanda) is the input side
Olive (person) is the output
side
Light ray travels from right to left
-
Fish (Wanda) is the input side
Olive (person) is the output
side
Light ray travels from right to left
𝑛𝑜𝑢𝑡𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
Free spacepropagation air
(𝑠)
Refractionat
spherical surface (R)
Free spacepropagation inside water
(𝑠′)
𝑛𝑖𝑛𝛼𝑖𝑛𝑥𝑖𝑛
From Output side to Input side
-
Fish (Wanda) is the input side
Olive (person) is the output
side
Light ray travels from right to left
𝑛𝑜𝑢𝑡𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
Free spacepropagation air
(𝑠)
Refractionat
spherical surface (R)
Free spacepropagation inside water
(𝑠′)
𝑛𝑖𝑛𝛼𝑖𝑛𝑥𝑖𝑛
Here, 𝑛𝑜𝑢𝑡 = 1 and 𝑛𝑖𝑛 = 𝑛Hence:
𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
Free spacepropagation air
(𝑠)
Refractionat
spherical surface (R)
Free spacepropagation inside water
(𝑠′)
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
From Output side to Input side
-
𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
Free spacepropagation air
(𝑠)
Refractionat
spherical surface (R)
Free spacepropagation inside water
(𝑠′)
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
-
𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
Free spacepropagation air
(𝑠)
Refractionat
spherical surface (R)
Free spacepropagation inside water
(𝑠′)
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
1 0𝐷
𝑛1
Free space propagation
matrix
1 −𝑛𝑜𝑢𝑡 − 𝑛𝑖𝑛
𝑅0 1
Refraction at spherical surface
matrix
-
𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
Free spacepropagation air
(𝑠)
Refractionat
spherical surface (R)
Free spacepropagation inside water
(𝑠′)
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
1 0𝐷
𝑛1
Free space propagation
matrix
1 −𝑛𝑜𝑢𝑡 − 𝑛𝑖𝑛
𝑅0 1
Refraction at spherical surface
matrix
𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 0𝑠 1
1 −1−𝑛
−𝑅
0 1
1 0𝑅
𝑛1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
(since 𝑠′ = 𝑅)
-
𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
Free spacepropagation air
(𝑠)
Refractionat
spherical surface (R)
Free spacepropagation inside water
(𝑠′)
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
1 0𝐷
𝑛1
Free space propagation
matrix
1 −𝑛𝑜𝑢𝑡 − 𝑛𝑖𝑛
𝑅0 1
Refraction at spherical surface
matrix
𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 0𝑠 1
1 −1−𝑛
−𝑅
0 1
1 0𝑅
𝑛1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
(since 𝑠′ = 𝑅)
𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 0𝑠 1
1 +1−𝑛
𝑅
𝑅
𝑛
1−𝑛
𝑅𝑅
𝑛1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
-
𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
Free spacepropagation air
(𝑠)
Refractionat
spherical surface (R)
Free spacepropagation inside water
(𝑠′)
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
1 0𝐷
𝑛1
Free space propagation
matrix
1 −𝑛𝑜𝑢𝑡 − 𝑛𝑖𝑛
𝑅0 1
Refraction at spherical surface
matrix
𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 0𝑠 1
1 −1−𝑛
−𝑅
0 1
1 0𝑅
𝑛1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
(since 𝑠′ = 𝑅)
𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 0𝑠 1
1 +1−𝑛
𝑅
𝑅
𝑛
1−𝑛
𝑅𝑅
𝑛1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 0𝑠 1
1
𝑛
1 − 𝑛
𝑅𝑅
𝑛1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
-
𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
Free spacepropagation air
(𝑠)
Refractionat
spherical surface (R)
Free spacepropagation inside water
(𝑠′)
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
1 0𝐷
𝑛1
Free space propagation
matrix
1 −𝑛𝑜𝑢𝑡 − 𝑛𝑖𝑛
𝑅0 1
Refraction at spherical surface
matrix
𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 0𝑠 1
1 −1−𝑛
−𝑅
0 1
1 0𝑅
𝑛1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
(since 𝑠′ = 𝑅)
𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 0𝑠 1
1 +1−𝑛
𝑅
𝑅
𝑛
1−𝑛
𝑅𝑅
𝑛1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 0𝑠 1
1
𝑛
1 − 𝑛
𝑅𝑅
𝑛1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
1
𝑛
1 − 𝑛
𝑅𝑠
𝑛+𝑅
𝑛𝑠1 − 𝑛
𝑅+ 1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
-
𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
Free spacepropagation air
(𝑠)
Refractionat
spherical surface (R)
Free spacepropagation inside water
(𝑠′)
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
1 0𝐷
𝑛1
Free space propagation
matrix
1 −𝑛𝑜𝑢𝑡 − 𝑛𝑖𝑛
𝑅0 1
Refraction at spherical surface
matrix
𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 0𝑠 1
1 −1−𝑛
−𝑅
0 1
1 0𝑅
𝑛1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
(since 𝑠′ = 𝑅)
𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 0𝑠 1
1 +1−𝑛
𝑅
𝑅
𝑛
1−𝑛
𝑅𝑅
𝑛1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 0𝑠 1
1
𝑛
1 − 𝑛
𝑅𝑅
𝑛1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
1
𝑛
1 − 𝑛
𝑅𝑠
𝑛+𝑅
𝑛𝑠1 − 𝑛
𝑅+ 1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
Imaging Condition: M21 = 0
𝑠
𝑛+𝑅
𝑛= 0
𝑠 = −𝑅
-
Fish (Wanda) is the output
side
Olive (person) is the input
side
Light ray travels from left to right
-
Fish (Wanda) is the output
side
Olive (person) is the input
side
Light ray travels from left to right
𝑛𝑜𝑢𝑡𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
Free spacepropagation inside water
(𝑠′)
Refractionat
spherical surface (R)
Free spacepropagation in air
(𝑠)
𝑛𝑖𝑛𝛼𝑖𝑛𝑥𝑖𝑛
From Output side to Input side
-
Fish (Wanda) is the output
side
Olive (person) is the input
side
Light ray travels from left to right
𝑛𝑜𝑢𝑡𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
Free spacepropagation inside water
(𝑠′)
Refractionat
spherical surface (R)
Free spacepropagation in air
(𝑠)
𝑛𝑖𝑛𝛼𝑖𝑛𝑥𝑖𝑛
Here, 𝑛𝑜𝑢𝑡 = 𝑛 and 𝑛𝑖𝑛 = 1Hence:
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
Free spacepropagation inside water
(𝑠′)
Refractionat
spherical surface (R)
Free spacepropagation in air
(𝑠)
𝛼𝑖𝑛𝑥𝑖𝑛
From Output side to Input side
-
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
Free spacepropagation inside water
(𝑠′)
Refractionat
spherical surface (R)
Free spacepropagation in air
(𝑠)
𝛼𝑖𝑛𝑥𝑖𝑛
-
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
Free spacepropagation inside water
(𝑠′)
Refractionat
spherical surface (R)
Free spacepropagation in air
(𝑠)
𝛼𝑖𝑛𝑥𝑖𝑛
1 0𝐷
𝑛1
Free space propagation
matrix
1 −𝑛𝑜𝑢𝑡 − 𝑛𝑖𝑛
𝑅0 1
Refraction at spherical surface
matrix
-
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
Free spacepropagation inside water
(𝑠′)
Refractionat
spherical surface (R)
Free spacepropagation in air
(𝑠)
𝛼𝑖𝑛𝑥𝑖𝑛
1 0𝐷
𝑛1
Free space propagation
matrix
1 −𝑛𝑜𝑢𝑡 − 𝑛𝑖𝑛
𝑅0 1
Refraction at spherical surface
matrix
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 0𝑠′
𝑛1
1 −𝑛−1
𝑅
0 1
1 0𝑠 1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
(since 𝑠′ = 𝑅)
-
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
Free spacepropagation inside water
(𝑠′)
Refractionat
spherical surface (R)
Free spacepropagation in air
(𝑠)
𝛼𝑖𝑛𝑥𝑖𝑛
1 0𝐷
𝑛1
Free space propagation
matrix
1 −𝑛𝑜𝑢𝑡 − 𝑛𝑖𝑛
𝑅0 1
Refraction at spherical surface
matrix
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 0𝑠′
𝑛1
1 −𝑛−1
𝑅
0 1
1 0𝑠 1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
(since 𝑠′ = 𝑅)
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 0𝑠′
𝑛1
1 + 𝑠1 − 𝑛
𝑅
1 − 𝑛
𝑅𝑠 1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
-
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
Free spacepropagation inside water
(𝑠′)
Refractionat
spherical surface (R)
Free spacepropagation in air
(𝑠)
𝛼𝑖𝑛𝑥𝑖𝑛
1 0𝐷
𝑛1
Free space propagation
matrix
1 −𝑛𝑜𝑢𝑡 − 𝑛𝑖𝑛
𝑅0 1
Refraction at spherical surface
matrix
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 0𝑠′
𝑛1
1 −𝑛−1
𝑅
0 1
1 0𝑠 1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
(since 𝑠′ = 𝑅)
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 0𝑠′
𝑛1
1 + 𝑠1 − 𝑛
𝑅
1 − 𝑛
𝑅𝑠 1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
1 + 𝑠1 − 𝑛
𝑅
1 − 𝑛
𝑅𝑠′
𝑛1 + 𝑠
1 − 𝑛
𝑅+ 𝑠
𝑠′
𝑛
1 − 𝑛
𝑅+ 1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
-
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
Free spacepropagation inside water
(𝑠′)
Refractionat
spherical surface (R)
Free spacepropagation in air
(𝑠)
𝛼𝑖𝑛𝑥𝑖𝑛
1 0𝐷
𝑛1
Free space propagation
matrix
1 −𝑛𝑜𝑢𝑡 − 𝑛𝑖𝑛
𝑅0 1
Refraction at spherical surface
matrix
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 0𝑠′
𝑛1
1 −𝑛−1
𝑅
0 1
1 0𝑠 1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
(since 𝑠′ = 𝑅)
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 0𝑠′
𝑛1
1 + 𝑠1 − 𝑛
𝑅
1 − 𝑛
𝑅𝑠 1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
1 + 𝑠1 − 𝑛
𝑅
1 − 𝑛
𝑅𝑠′
𝑛1 + 𝑠
1 − 𝑛
𝑅+ 𝑠
𝑠′
𝑛
1 − 𝑛
𝑅+ 1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 + 𝑠
1 − 𝑛
𝑅
1 − 𝑛
𝑅𝑠′
𝑛+ 𝑠 +
𝑠𝑠′
𝑛𝑅(1 − 𝑛) 1 +
𝑠′
𝑛𝑅(1 − 𝑛)
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
-
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
Free spacepropagation inside water
(𝑠′)
Refractionat
spherical surface (R)
Free spacepropagation in air
(𝑠)
𝛼𝑖𝑛𝑥𝑖𝑛
1 0𝐷
𝑛1
Free space propagation
matrix
1 −𝑛𝑜𝑢𝑡 − 𝑛𝑖𝑛
𝑅0 1
Refraction at spherical surface
matrix
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 0𝑠′
𝑛1
1 −𝑛−1
𝑅
0 1
1 0𝑠 1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
(since 𝑠′ = 𝑅)
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 0𝑠′
𝑛1
1 + 𝑠1 − 𝑛
𝑅
1 − 𝑛
𝑅𝑠 1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
1 + 𝑠1 − 𝑛
𝑅
1 − 𝑛
𝑅𝑠′
𝑛1 + 𝑠
1 − 𝑛
𝑅+ 𝑠
𝑠′
𝑛
1 − 𝑛
𝑅+ 1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 + 𝑠
1 − 𝑛
𝑅
1 − 𝑛
𝑅𝑠′
𝑛+ 𝑠 +
𝑠𝑠′
𝑛𝑅(1 − 𝑛) 1 +
𝑠′
𝑛𝑅(1 − 𝑛)
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
-
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
Free spacepropagation inside water
(𝑠′)
Refractionat
spherical surface (R)
Free spacepropagation in air
(𝑠)
𝛼𝑖𝑛𝑥𝑖𝑛
1 0𝐷
𝑛1
Free space propagation
matrix
1 −𝑛𝑜𝑢𝑡 − 𝑛𝑖𝑛
𝑅0 1
Refraction at spherical surface
matrix
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 0𝑠′
𝑛1
1 −𝑛−1
𝑅
0 1
1 0𝑠 1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
(since 𝑠′ = 𝑅)
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 0𝑠′
𝑛1
1 + 𝑠1 − 𝑛
𝑅
1 − 𝑛
𝑅𝑠 1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=
1 + 𝑠1 − 𝑛
𝑅
1 − 𝑛
𝑅𝑠′
𝑛1 + 𝑠
1 − 𝑛
𝑅+ 𝑠
𝑠′
𝑛
1 − 𝑛
𝑅+ 1
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡
=1 + 𝑠
1 − 𝑛
𝑅
1 − 𝑛
𝑅𝑠′
𝑛+ 𝑠 +
𝑠𝑠′
𝑛𝑅(1 − 𝑛) 1 +
𝑠′
𝑛𝑅(1 − 𝑛)
𝑛𝛼𝑖𝑛𝑥𝑖𝑛
Imaging Condition: M21 = 0
𝑠′
𝑛+ 𝑠 +
𝑠𝑠′
𝑛𝑅(1 − 𝑛) = 0