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[2]
(d) luminosity depends on temperature;
luminosity depends on area/radius;
so different temperatures can have different luminosities / graph does not include
area; [3]
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F2. (a) apparent magnitude is a measure of how bright an object appears (from Earth);
absolute magnitude is a measure of, how bright an object appears / the apparent
magnitude, when observed from a distance of 10pc ; [2]
L bA LAdB2
(b) (i) b ;
4 d2 bB LBdA2
bALB
rearrange to give dB dA ;
bBLA
substitution to give dB 25dA ; (hence 500pc ) [3]
(ii) if star A was at 10 pc, it would be 100 times brighter (because brightness scales
2
with d );
so absolute magnitude is five below the apparent magnitude; (hence 0.0) [2]
N.B. Award maximum credit for detailed calculation leading to correct answer.
F3. (a) light from distant galaxies/stars is red-shifted / existence of CMB / interstellar gas
temperature in distant galaxies is 3K ; [1]
(b) (i) the critical density is the density of the Universe that would be necessary to
stop the expansion after an infinite amount of time; [1]
Do not accept answers based on the density at which the universe is flat .
(ii) whether the universe will expand forever or close back in on itself is determined
by the comparison of these values;
at low density, the universe will continue to expand forever;
at high densities, the universe will stop expanding and then contract /
eventually contract; [3]
Award of second and third marks means, by implication, that the first has been
scored.
15 M07/4/PHYSI/SP3/ENG/TZ1XX/M+
Option G Relativity
G1. (a) the detector drawn some distance away from the original pair and off to the left;
Accept indication with arrow(s).
a light beam symmetric about a vertical line passing through the point where the
beam hits the mirror joining the emitter and detector; [2]
(b)
vt
identifies triangle with a base equal to and height d ;
(b)
2
d
vt
2
application of Pythagoras theorem;
total path twice hypoteneuse; [3]
16 M07/4/PHYSI/SP3/ENG/TZ1XX/M+
2d
(c) (i) t0 ; [1]
c
(ii) observed time,
2
vt
2
2 d
L 2
t ;
cc
rearrange to give
2
t2(c2 v2) 4d ;
thus
2d 1
t ; [3]
c
v2
1
c2
t0
and hence t
v2
1
c2
G2. light from clock A travels further to Frank than light from clock B;
at the same constant speed c / speed of light is same for both observers;
light from clock A takes longer to reach Frank / if Frank observes clock A change to 1,
clock B will already have changed;
therefore, clocks do not read the same time;
or
events are simultaneous to Albert;
so cannot be simultaneous in a different/Frank s frame of reference;
light from B travels shorter distance at speed c;
so B changes first/runs faster; [4]
G3. (a) if the muon measures 4500m in its reference frame; recognizes the idea of two
frames of reference
1
the muon/Earth would have to travel at 2.0 109 ms / faster than the speed of light;
which is not possible;
distance travelled, as measured in muon s reference frame must be less/contracted; [4]
(b) mc2 Ve m0c2 ;
210MeV 105MeV
315MeV;
m 315MeVc or 3m0 ; [3]
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Option H Optics
H1. (a) light (that is a combination of colors/wavelengths/frequencies) is divided/split into its
component colours/wavelengths/frequencies; [1]
(b)
bends towards the normal at first surface;
away from normal at second;
blue is deviated to a greater degree than red at both interfaces; [3]
Normals do not need to be drawn.
Award [1 max] if dispersion is shown at second face only.
(c) refraction angle for blue light is less than for red light (at the first boundary);
sin i
since n ;
sin r
n for blue is greater / n for red is less; [3]
Do not award marks for bald answers or answers with fallacious argument.
Allow ECF for consistent argument for switching of B and R from (b).
(d) recombined / white light;
parallel to the incoming beam; [2]
ignore displacement and/or rays within block
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H2. (a) one ray through the optical centre of the lens;
one through a focal point;
back traced to locate image; [3]
No need for arrows or dotted lines
(b) virtual, magnified, erect; [2]
Award [2] for all three and [1] for any two.
(c)
A between object and objective, and equidistant on opposite side of lens;
B located between two lenses;
C located (just) further from eyepiece lens than B, and equidistant on opposite side;
do not allow if B is not between lenses
D located near O; accept anywhere to the left of the objective [4]
Rays do not need be drawn.
(d) less distortion;
less chromatic aberration; [2]
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