Introduction to Geometrical Optics: Sample problems ...€¦ · Introduction to Geometrical Optics: Sample problems solutions supplementary slides Apratim Majumder Optics for Energy

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



side


𝑛𝑜𝑢𝑡𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡

=

Free spacepropagation air

(𝑠)

Refractionat

spherical surface (R)

Free spacepropagation inside water

(𝑠′)

𝑛𝑖𝑛𝛼𝑖𝑛𝑥𝑖𝑛

From Output side to Input side



side



=


(𝑠)

Refractionat



(𝑠′)


Here, 𝑛𝑜𝑢𝑡 = 1 and 𝑛𝑖𝑛 = 𝑛Hence:

𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡

=


(𝑠)

Refractionat



(𝑠′)

𝑛𝛼𝑖𝑛𝑥𝑖𝑛



=


(𝑠)

Refractionat



(𝑠′)



=


(𝑠)

Refractionat



(𝑠′)


1 0𝐷

𝑛1

Free space propagation

matrix

1 −𝑛𝑜𝑢𝑡 − 𝑛𝑖𝑛

𝑅0 1

Refraction at spherical surface

matrix


=


(𝑠)

Refractionat



(𝑠′)


1 0𝐷

𝑛1


matrix


𝑅0 1


matrix


=1 0𝑠 1

1 −1−𝑛

−𝑅

0 1

1 0𝑅

𝑛1


(since 𝑠′ = 𝑅)


=


(𝑠)

Refractionat



(𝑠′)


1 0𝐷

𝑛1


matrix


𝑅0 1


matrix


=1 0𝑠 1

1 −1−𝑛

−𝑅

0 1

1 0𝑅

𝑛1




=1 0𝑠 1

1 +1−𝑛

𝑅

𝑅

𝑛

1−𝑛

𝑅𝑅

𝑛1



=


(𝑠)

Refractionat



(𝑠′)


1 0𝐷

𝑛1


matrix


𝑅0 1


matrix


=1 0𝑠 1

1 −1−𝑛

−𝑅

0 1

1 0𝑅

𝑛1




=1 0𝑠 1

1 +1−𝑛

𝑅

𝑅

𝑛

1−𝑛

𝑅𝑅

𝑛1



=1 0𝑠 1

1

𝑛

1 − 𝑛

𝑅𝑅

𝑛1



=


(𝑠)

Refractionat



(𝑠′)


1 0𝐷

𝑛1


matrix


𝑅0 1


matrix


=1 0𝑠 1

1 −1−𝑛

−𝑅

0 1

1 0𝑅

𝑛1




=1 0𝑠 1

1 +1−𝑛

𝑅

𝑅

𝑛

1−𝑛

𝑅𝑅

𝑛1



=1 0𝑠 1

1

𝑛

1 − 𝑛

𝑅𝑅

𝑛1



=

1

𝑛

1 − 𝑛

𝑅𝑠

𝑛+𝑅

𝑛𝑠1 − 𝑛

𝑅+ 1



=


(𝑠)

Refractionat



(𝑠′)


1 0𝐷

𝑛1


matrix


𝑅0 1


matrix


=1 0𝑠 1

1 −1−𝑛

−𝑅

0 1

1 0𝑅

𝑛1




=1 0𝑠 1

1 +1−𝑛

𝑅

𝑅

𝑛

1−𝑛

𝑅𝑅

𝑛1



=1 0𝑠 1

1

𝑛

1 − 𝑛

𝑅𝑅

𝑛1



=

1

𝑛

1 − 𝑛

𝑅𝑠

𝑛+𝑅

𝑛𝑠1 − 𝑛

𝑅+ 1


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


side


side



=


(𝑠′)

Refractionat


Free spacepropagation in air

(𝑠)




side


side



=


(𝑠′)

Refractionat



(𝑠)


Here, 𝑛𝑜𝑢𝑡 = 𝑛 and 𝑛𝑖𝑛 = 1Hence:

𝑛𝛼𝑜𝑢𝑡𝑥𝑜𝑢𝑡

=


(𝑠′)

Refractionat



(𝑠)

𝛼𝑖𝑛𝑥𝑖𝑛



=


(𝑠′)

Refractionat



(𝑠)



=


(𝑠′)

Refractionat



(𝑠)


1 0𝐷

𝑛1


matrix


𝑅0 1


matrix


=


(𝑠′)

Refractionat



(𝑠)


1 0𝐷

𝑛1


matrix


𝑅0 1


matrix


=1 0𝑠′

𝑛1

1 −𝑛−1

𝑅

0 1

1 0𝑠 1




=


(𝑠′)

Refractionat



(𝑠)


1 0𝐷

𝑛1


matrix


𝑅0 1


matrix


=1 0𝑠′

𝑛1

1 −𝑛−1

𝑅

0 1

1 0𝑠 1




=1 0𝑠′

𝑛1

1 + 𝑠1 − 𝑛

𝑅

1 − 𝑛

𝑅𝑠 1



=


(𝑠′)

Refractionat



(𝑠)


1 0𝐷

𝑛1


matrix


𝑅0 1


matrix


=1 0𝑠′

𝑛1

1 −𝑛−1

𝑅

0 1

1 0𝑠 1




=1 0𝑠′

𝑛1

1 + 𝑠1 − 𝑛

𝑅

1 − 𝑛

𝑅𝑠 1



=

1 + 𝑠1 − 𝑛

𝑅

1 − 𝑛

𝑅𝑠′

𝑛1 + 𝑠

1 − 𝑛

𝑅+ 𝑠

𝑠′

𝑛

1 − 𝑛

𝑅+ 1



=


(𝑠′)

Refractionat



(𝑠)


1 0𝐷

𝑛1


matrix


𝑅0 1


matrix


=1 0𝑠′

𝑛1

1 −𝑛−1

𝑅

0 1

1 0𝑠 1




=1 0𝑠′

𝑛1

1 + 𝑠1 − 𝑛

𝑅

1 − 𝑛

𝑅𝑠 1



=

1 + 𝑠1 − 𝑛

𝑅

1 − 𝑛

𝑅𝑠′

𝑛1 + 𝑠

1 − 𝑛

𝑅+ 𝑠

𝑠′

𝑛

1 − 𝑛

𝑅+ 1



=1 + 𝑠

1 − 𝑛

𝑅

1 − 𝑛

𝑅𝑠′

𝑛+ 𝑠 +

𝑠𝑠′

𝑛𝑅(1 − 𝑛) 1 +

𝑠′

𝑛𝑅(1 − 𝑛)



=


(𝑠′)

Refractionat



(𝑠)


1 0𝐷

𝑛1


matrix


𝑅0 1


matrix


=1 0𝑠′

𝑛1

1 −𝑛−1

𝑅

0 1

1 0𝑠 1




=1 0𝑠′

𝑛1

1 + 𝑠1 − 𝑛

𝑅

1 − 𝑛

𝑅𝑠 1



=

1 + 𝑠1 − 𝑛

𝑅

1 − 𝑛

𝑅𝑠′

𝑛1 + 𝑠

1 − 𝑛

𝑅+ 𝑠

𝑠′

𝑛

1 − 𝑛

𝑅+ 1



=1 + 𝑠

1 − 𝑛

𝑅

1 − 𝑛

𝑅𝑠′

𝑛+ 𝑠 +

𝑠𝑠′

𝑛𝑅(1 − 𝑛) 1 +

𝑠′

𝑛𝑅(1 − 𝑛)


Imaging Condition: M21 = 0

𝑠′

𝑛+ 𝑠 +

𝑠𝑠′

𝑛𝑅(1 − 𝑛) = 0

Introduction to Geometrical Optics: Sample problems ...€¦ · Introduction to Geometrical Optics: Sample problems solutions supplementary slides Apratim Majumder Optics for Energy

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