The refractive index n of a substance is a dimensionless measure of how much light bends (refracts) when passing from one medium to another. n = c v where c is the speed of light in a vacuum (a constant) and v is the speed of light in the medium. For example, the refractive index of diamond is 2.42 which means that light travels 2.42 times as fast in a vacuum as it does in a diamond. Snell's law is an equation that relates the indices of refraction of two different mediums to the angle of incidence θ 1 and angle of refraction θ 2 . Angles θ 1 and θ 2 are measured from a line perpendicular to the boundary between the two mediums. Use this relationship and the table of refraction indices to complete Exercises 93-94. n 1 s i n θ 1 , = n 2 sin θ 2 Assume that a beam of light travels from air into water. a. If the incidence angle θ 1 is 40 ∘ , what is the angle of refraction θ 2 ? Round to the nearest tenth of a degree. b. Alina attempts to spear a lobster from her boat, if she aims her spear directly at the lobster, will she hit it? Explain your answer.
The refractive index n of a substance is a dimensionless measure of how much light bends (refracts) when passing from one medium to another. n = c v where c is the speed of light in a vacuum (a constant) and v is the speed of light in the medium. For example, the refractive index of diamond is 2.42 which means that light travels 2.42 times as fast in a vacuum as it does in a diamond. Snell's law is an equation that relates the indices of refraction of two different mediums to the angle of incidence θ 1 and angle of refraction θ 2 . Angles θ 1 and θ 2 are measured from a line perpendicular to the boundary between the two mediums. Use this relationship and the table of refraction indices to complete Exercises 93-94. n 1 s i n θ 1 , = n 2 sin θ 2 Assume that a beam of light travels from air into water. a. If the incidence angle θ 1 is 40 ∘ , what is the angle of refraction θ 2 ? Round to the nearest tenth of a degree. b. Alina attempts to spear a lobster from her boat, if she aims her spear directly at the lobster, will she hit it? Explain your answer.
Solution Summary: The author explains Snell's law, which relates the indices of retion of two different mediums to the angle of incidence
The refractive index
n
of a substance is a dimensionless measure of how much light bends (refracts) when passing from one medium to another.
n
=
c
v
where
c
is the speed of light in a vacuum (a constant) and
v
is the speed of light in the medium. For example, the refractive index of diamond is 2.42 which means that light travels 2.42 times as fast in a vacuum as it does in a diamond.
Snell's law is an equation that relates the indices of refraction of two different mediums to the angle of incidence
θ
1
and angle of refraction
θ
2
. Angles
θ
1
and
θ
2
are measured from a line perpendicular to the boundary between the two mediums. Use this relationship and the table of refraction indices to complete Exercises 93-94.
n
1
s
i
n
θ
1
,
=
n
2
sin
θ
2
Assume that a beam of light travels from air into water.
a. If the incidence angle
θ
1
is
40
∘
, what is the angle of refraction
θ
2
? Round to the nearest tenth of a degree.
b. Alina attempts to spear a lobster from her boat, if she aims her spear directly at the lobster, will she hit it? Explain your answer.
Given lim x-4 f (x) = 1,limx-49 (x) = 10, and lim→-4 h (x) = -7 use the limit properties
to find lim→-4
1
[2h (x) — h(x) + 7 f(x)] :
-
h(x)+7f(x)
3
O DNE
17. Suppose we know that the graph below is the graph of a solution to dy/dt = f(t).
(a) How much of the slope field can
you sketch from this information?
[Hint: Note that the differential
equation depends only on t.]
(b) What can you say about the solu-
tion with y(0) = 2? (For example,
can you sketch the graph of this so-
lution?)
y(0) = 1
y
AN
(b) Find the (instantaneous) rate of change of y at x = 5.
In the previous part, we found the average rate of change for several intervals of decreasing size starting at x = 5. The instantaneous rate of
change of fat x = 5 is the limit of the average rate of change over the interval [x, x + h] as h approaches 0. This is given by the derivative in the
following limit.
lim
h→0
-
f(x + h) − f(x)
h
The first step to find this limit is to compute f(x + h). Recall that this means replacing the input variable x with the expression x + h in the rule
defining f.
f(x + h) = (x + h)² - 5(x+ h)
=
2xh+h2_
x² + 2xh + h² 5✔
-
5
)x - 5h
Step 4
-
The second step for finding the derivative of fat x is to find the difference f(x + h) − f(x).
-
f(x + h) f(x) =
= (x²
x² + 2xh + h² -
])-
=
2x
+ h² - 5h
])x-5h) - (x² - 5x)
=
]) (2x + h - 5)
Macbook Pro
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY