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Question 23M.3.HL.TZ1.13

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Date May 2023 Marks available [Maximum mark: 10] Reference code 23M.3.HL.TZ1.13
Level HL Paper 3 Time zone TZ1
Command term Calculate, Determine, Show that, Sketch, State Question number 13 Adapted from N/A
13.
[Maximum mark: 10]
23M.3.HL.TZ1.13

A ray of monochromatic light is incident on an optical fibre making an angle of θ with the normal. The refractive index of the core is 1.500 and the refractive index of the cladding is 1.489.

(a.i)

Calculate the critical angle θc at the core-cladding boundary.

[2]

Markscheme

1.500 × sin θc = 14.89 × 1 ✓

θc = 83.06° ✓

 

Allow 83° OR 1.45 rad.

Examiners report

Signal transmitted by optical fibre. Average students used Ray optics well.

(a.ii)

Determine the maximum value of θ such that the ray is incident on the core-cladding boundary at an angle greater than the critical angle.

[2]

Markscheme

1.00 × sin θmax = 1.500 × sin(90° − 83.06°) ✓

θmax = 10.4° ✓

 

Allow 11°

Allow ECF from (a)(i).

(b)

The diagram shows two rays following different paths in the optical fibre. Ray 1 travels along the axis of the fibre. Ray 2 is incident on the core-cladding boundary at an angle φ just greater than θc.

The length of the optical fibre is 1 km. Show that the time delay between the arrival of the two rays at the end of the optical fibre is about 37 ns.

[3]

Markscheme

« when ray 1 travels a distance 1.00 km » ray 2 travels a distance 1sin θc = 1.0074 km ✓

speed is = c1.500 = 2.0 × 108 «m s−1» ✓

hence Δt = «0.0074 × 1032×108 =» 36.67 «ns»

 

Allow ECF from (a)(i).

Time for ray 1 is 5000 ns, time for ray 2 is 5036.9 ns.

Do not allow ECF from MP2.

For MP3, working or answer to at least 3 SF should be seen.

Examiners report

The path and time shift in b) was well calculated only by the best students. 

(c)

A signal transmitted by the optical fibre consists of very narrow digital pulses. The pulses are 37 ns apart. The graph shows the variation with time of the amplitude of two consecutive pulses input to the optical fibre.

(c.i)

Sketch, on the axes, the variation with time of the amplitude of the two pulses after they have travelled by all possible ray paths along a 1 km length of the optical fibre.

[2]

Markscheme

pulses rounded and of lower amplitude, symmetrical about dotted lines. ✓

just starting to overlap ✓

Examiners report

Also, only the best students used the concept of dispersion well in c).

(c.ii)

State what would happen when the input pulses are separated by less than 37 ns.

[1]

Markscheme

the pulses would overlap/the signal will be lost/OWTTE ✓