Points: 30

Time: 5.0 Hours

Geometry of Water Fountain
Part A: Uniformly Distributed Holes on the Surface of the Hemisphere
A.1[0.5pt]Write your working here or on the blank answer page for this question. Working written on theblank draft sheet will not be marked.
x(t) =y(t) =APHO 2024
Theory Answer Sheet, English (Official)

Page 1 of 35

Points: 30

A.2

Time: 5.0 Hoursy(x, θ) =[1.0pt]APHO 2024
Theory Answer Sheet, English (Official)

Page 2 of 35

Points: 30

A.3

Time: 5.0 Hoursy =[3.0pt]APHO 2024Theory Answer Sheet, English (Official)

Page 3 of 35

Points: 30

Time: 5.0 Hours

A.3[cont.]

APHO 2024
Theory Answer Sheet, English (Official)

Page 4 of 35

Points: 30

A.4

Time: 5.0 Hours

R(θ) =[1.0pt]APHO 2024
Theory Answer Sheet, English (Official)

Page 5 of 35

Points: 30

Time: 5.0 Hours

A.5[0.5pt]

APHO 2024
Theory Answer Sheet, English (Official)

Page 6 of 35

Points: 30

Time: 5.0 Hours

Part B: Non-Uniformly Distributed Holes on the Surface of the Hemisphere
B.1dAW =[1.0pt]APHO 2024
Theory Answer Sheet, English (Official)

Page 7 of 35

Points: 30

B.2

Time: 5.0 Hours∝ρ(θ)[2.0pt]APHO 2024
Theory Answer Sheet, English (Official)

Page 8 of 35

Points: 30

B.3

Time: 5.0 Hours∝ρ(θ)[1.0pt]APHO 2024
Theory Answer Sheet, English (Official)

Page 9 of 35

Points: 30

Time: 5.0 Hours

B.3[cont.]APHO 2024
Theory Answer Sheet, English (Official)

Page 10 of 35

Points: 30

Time: 5.0 Hours

Question 1 - Extra Answer Page
Additional working for question 1 included here will be marked. If you need more space forquestion 1, please ask an invigilator for a boxed sheet.
Clearly write which part of the question you are attempting.

APHO 2024
Theory Answer Sheet, English (Official)

Page 11 of 35

Points: 30

Time: 5.0 Hours

Snell's Law
Part A: Light Propagation Through a Semi-Sphere
A.1[0.5pt]Write your working here or on the blank answer page for this question. Working written on theblank draft sheet will not be marked.
Ray _____ propagates faster in the semi-sphere.

APHO 2024
Theory Answer Sheet, English (Official)

Page 12 of 35

Points: 30A.2

Time: 5.0 Hours

The difference between refractive index of ray a and ray b in the semi-sphere is _____[1.0pt]APHO 2024
Theory Answer Sheet, English (Official)

Page 13 of 35

Points: 30

Time: 5.0 Hours

Part B: Light Propagation Through a Cylindrical Rod
B.1

The incident angle, θ, where light is totally reflected back to the polymer is ___< θ <___.

[2.0pt]APHO 2024
Theory Answer Sheet, English (Official)

Page 14 of 35

Points: 30

Time: 5.0 Hours

B.2

When the other, open end of the rod is now coated with a thick layer of oil, with refractive index of 1.60.

(i)_________________________[0.6pt]APHO 2024
Theory Answer Sheet, English (Official)

Page 15 of 35

Points: 30

B.2

When the setup is placed in water,(ii)_________________________

Time: 5.0 Hours[0.9pt]APHO 2024
Theory Answer Sheet, English (Official)

Page 16 of 35

Points: 30

Time: 5.0 Hours

Part C: Light Propagation Through an Optical Fibre
C.1

The relationship between the acceptance angle θ and refractive indices is __________.
a[2.0pt]

APHO 2024
Theory Answer Sheet, English (Official)

Page 17 of 35

Points: 30

Time: 5.0 Hours

C.1[cont.]

APHO 2024
Theory Answer Sheet, English (Official)

Page 18 of 35

Points: 30

C.2

Time: 5.0 Hours

The new acceptance angle when the bending radius is 1 cm is ______________.

[2.6pt]APHO 2024
Theory Answer Sheet, English (Official)

Page 19 of 35

Points: 30

Time: 5.0 Hours

C.2[cont.]

APHO 2024
Theory Answer Sheet, English (Official)

Page 20 of 35

Points: 30

C.3

The maximum acceptance angle for case C.1 is _______,[0.4pt]and the maximum acceptance angle for case C.2 is _______.

APHO 2024
Theory Answer Sheet, English (Official)

Time: 5.0 Hours

Page 21 of 35

Points: 30

Time: 5.0 Hours

Question 2 - Extra Answer Page
Additional working for question 2 included here will be marked. If you need more space forquestion 2, please ask an invigilator for a boxed sheet.
Clearly write which part of the question you are attempting.

APHO 2024
Theory Answer Sheet, English (Official)

Page 22 of 35

Points: 30

Time: 5.0 Hours

The First Discovered Quasar: Unveiling theMysteries of the Astrophysical Source 3C 273
Part A: Moon's Apparent Motion Against the Background Stars
A.1[1.3pt]Write your working here or on the blank answer page for this question. Working written on theblank draft sheet will not be marked.

APHO 2024
Theory Answer Sheet, English (Official)

Page 23 of 35

Points: 30

Time: 5.0 Hours

A.2[0.5pt]APHO 2024
Theory Answer Sheet, English (Official)

Page 24 of 35

Points: 30

Time: 5.0 Hours

Part B: Using Lunar Occultations to Precisely Determine Radio Source Positions: The Case of 3C273
B.1[0.6pt]APHO 2024
Theory Answer Sheet, English (Official)

Page 25 of 35

Points: 30

Time: 5.0 Hours

B.2[0.6pt]B.3[0.6pt]APHO 2024
Theory Answer Sheet, English (Official)

Page 26 of 35

Points: 30

Time: 5.0 Hours

Part C: The Breakthrough Discovery of 3C 273's True Nature
C.1[0.6pt]APHO 2024
Theory Answer Sheet, English (Official)

Page 27 of 35

Points: 30

Time: 5.0 Hours

C.2[0.6pt]C.3[0.6pt]APHO 2024
Theory Answer Sheet, English (Official)

Page 28 of 35

Points: 30

Time: 5.0 Hours

Part D: The Intrinsic Luminosity of the Radio Source 3C 273
D.1[0.6pt]APHO 2024
Theory Answer Sheet, English (Official)

Page 29 of 35

Points: 30

Time: 5.0 Hours

D.2[0.6pt]D.3[0.6pt]APHO 2024
Theory Answer Sheet, English (Official)

Page 30 of 35

Points: 30

Time: 5.0 Hours

Part E: The Power Source of 3C 273
E.1[0.7pt]APHO 2024
Theory Answer Sheet, English (Official)

Page 31 of 35

Points: 30

Time: 5.0 Hours

E.2[0.7pt]APHO 2024
Theory Answer Sheet, English (Official)

Page 32 of 35

Points: 30

Time: 5.0 Hours

Part F: Modern Observations and the Nature of 3C 273's Components
F.1[0.7pt]APHO 2024
Theory Answer Sheet, English (Official)

Page 33 of 35

Points: 30

Time: 5.0 Hours

F.2[0.7pt]APHO 2024
Theory Answer Sheet, English (Official)

Page 34 of 35

Points: 30

Time: 5.0 Hours

Question 3 - Extra Answer Page
Additional working for question 3 included here will be marked. If you need more space forquestion 3, please ask an invigilator for a boxed sheet.
Clearly write which part of the question you are attempting.

APHO 2024
Theory Answer Sheet, English (Official)

Page 35 of 35