mehta (snm425) – Homework 1 – erskine – (58715)
1
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printout
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have
21
questions.
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before answering.
001
(part 1 of 3) 10.0 points
For 599 nm light, calculate the critical an
gle for the following materials surrounded by
water (index of refraction: 1
.
333). diamond.
(index of refraction: 2
.
34)
Correct answer: 34
.
7264
◦
.
Explanation:
Basic Concept:
Snell’s law for total internal reflection:
n
1
sin
θ
c
=
n
2
sin 90
◦
where
θ
c
is the critical angle for total internal
reflection. From Snell’s law, for total internal
reflection in diamond,
2
.
34 sin
θ
1
= 1
.
333 sin 90
◦
So, critical angle for for diamond
θ
diamond
= sin
−
1
parenleftbigg
1
.
333
2
.
34
parenrightbigg
= 34
.
7264
◦
.
002
(part 2 of 3) 10.0 points
flint glass. (index of refraction: 1
.
64)
Correct answer: 54
.
3709
◦
.
Explanation:
Similarly, critical angle for flint glass
θ
glass
= sin
−
1
parenleftbigg
1
.
333
1
.
64
parenrightbigg
= 54
.
3709
◦
.
003
(part 3 of 3) 10.0 points
ice. (index of refraction: 1
.
31)
1.
sin
−
1
parenleftbigg
n
water
n
ice
parenrightbigg
2.
there is no critical angle
correct
3.
sin
−
1
parenleftbigg
1
n
ice
parenrightbigg
4.
sin
−
1
parenleftbigg
n
ice
n
water
parenrightbigg
Explanation:
For ice, since its refraction index, 1
.
31, is
less than that of water, 1
.
333, there is no
critical angle!
004
10.0 points
Hint:
A ray diagram would be helpful.
Determine the minimum height of a vertical
flat mirror in which a person 71 in
.
in height
can see his or her full image.
Correct answer: 35
.
5 in
.
.
Explanation:
In the figure, the mirror is labeled
AB
.
A ray from the woman’s foot
F
strikes the
bottom of the mirror at
B
, with an angle
equal to
θ
and proceeds to the woman’s eye.
L
θ
θ
C
D
A
B
E
T
F
M
The two right triangles
EBM
and
FBM
are identical, since they share the common
side
MB
and angle
θ
. Therefore
EM
=
MF
=
1
2
EF
which is also the distance
BC
. Similarly, a ray
from the top of the woman’s head
T
strikes
the top of the mirror at
A
and proceeds to
her eye. The same line of reasoning as above
leads to the conclusion that
DA
=
1
2
TE
Thus the length
AB
of the mirror is
1
2
(
TE
+
EF
), which is one half the woman’s height.
Note that the mirror’s bottom edge must be
exactly
1
2
EF
from the floor for a fullheight
image to be possible.
Note also that the
conclusions reached here are valid regardless
of how far she stands from the mirror.
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mehta (snm425) – Homework 1 – erskine – (58715)
2
005
10.0 points
An object is placed at a distance of 1.5
f
from
a converging lens of focal length
f
, as shown.
2
f
f
f
2
f
3
f
What type of image is formed and what is
the size relative to the object?
Type
Size
Direction
1.
Virtual
Smaller
Inverted
2.
Real
Smaller
Upright
3.
Virtual
Smaller
Upright
4.
Virtual
Same size
Upright
5.
Real
Larger
Inverted
correct
6.
Real
Smaller
Inverted
7.
Virtual
Larger
Inverted
8.
Virtual
Larger
Upright
9.
Real
Larger
Upright
10.
Virtual
Same size
Inverted
Explanation:
Let :
p
= 1
.
5
f .
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 Spring '10
 ERSKINE
 Physics, Work, Light, Correct Answer, Mehta, Erskine

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