Now, find the angle θ4 shown in the figure (Figure 3) in terms of θ1 and α.
Express your answer in degrees in terms of θ1 and α.
The concepts related to this problem are the law of reflection and the triangle rule that related to the sum of the angles of a triangle.
Initially, find the relation between the anglesand
using the condition that the total angle made by the normal with the surface is equal to
. Later, use the law of reflection and equate the angles
and
. Then, we get the relation between the angles
and
. Later, use the condition that the sum of three angles of a triangle is equal to
and find a relation between
,
, and
. Later, eliminate the term
from this relation by using the relation between
and
. Then, the final equation contains the terms
,
, and
. Finally, rearrange the equation for
. This equation represents the required result.
The imaginary line which is normal to the common surface of two transparent media is called normal. The angle between the incidence ray and the normal is called angle of incidence and the angle between the reflected ray and the normal is called angle of reflection.
From the law of reflection, the angle of incidence is equal to the angle of reflection. In the figure, represents the angle of incidence at first incidence and
represents the corresponding angle of reflection. The terms
,
, and
represents the three angles of the triangle which is formed by one ray and two surfaces.
Use the law of reflection and find the relation betweenand
.
From the figure, the total angle made by the normal to the horizontal surface is equal to.
Substitutefor
.
From the rules of triangles, the sum of three angles of a triangle is equal to.
Use the equationin this equation, and rearrange the equation for
.
The expression for anglein terms of the angle
and the angle
is
.
Now, find the angle θ4 shown in the figure (Figure 3) in terms of θ1 and...
Find the angle θ6 shown in the figure (Figure 4) in
terms of θ1 and α. You will need to assume that
θ4<90∘, as it appears in the picture.
Express your answer in degrees in terms of θ1 and
α.
What is the smallest angle θ1 for which a laser beam will
undergo total internal reflection on the hypotenuse of the glass
prism in the figure?
Express your answer using two significant figures.
θ1 = ___ degrees
In the figure, light is incident at angle θ1 = 37.0˚ on a boundary between two transparent materials. Some of the light travels down through the next three layers of transparent materials, while some of it reflects upward and then escapes into the air. If n1 = 1.26, n2 = 1.42, n3 = 1.34 and n4 = 1.45, what is the value of (a) θ5 and (b) θ4?
In the figure, light is incident at angle θ1
= 37.0˚ on a boundary between two transparent materials. Some of
the light travels down through the next three layers of transparent
materials, while some of it reflects upward and then escapes into
the air. If n1 = 1.26, n2 =
1.36, n3 = 1.34and n4 =
1.45, what is the value of (a)
θ5 and (b)
θ4?
Air ns Y24
In the figure, light is incident at angle θ1 = 40.0° on a boundary between two transparent materials. Some of the light travels down through the next three layers of transparent materials, while some of it reflects upward and then escapes into the air. If n1 = 1.28, n2 = 1.36, n3 = 1.34 and n4 = 1.43, what is the value of (a) θ5 and (b) θ4? Air n1 7ng 74 (a) θ5_ Number Units (b) θ,-Number Units
Find the magnitude of tension in the two cords shown in the figure
(Figure 1) .
A) Neglect the mass of the cords, and assume
that the angle ? is 39 degrees and the mass m is
160 kg . What is the magnitude of the tension in the right
cord?
Express your answer using two significant figures and use the
following answer format: Fin right cord =______ N
B) What is the
magnitude of the tension in the left...
Constants A heavy flywheel is accelerated (rotationally) by a motor that provides constant torque and therefore a constant angular acceleration α. The flywheel is assumed to be at rest at time t=0 in Parts A and B of this problem. Find the time t1 it takes to accelerate the flywheel to ω1 if the angular acceleration is α. Express your answer in terms of ω1 and α t1 = ? Find the angle θ1 through which the flywheel will have...
Two plane mirrors are at an angle of θ1 = 69.4° with each other as in the side view shown in the figure below. If a horizontal ray is incident on mirror 1, at what angle θ2 does the outgoing reflected ray make with the surface of mirror 2?
A ray of light travels from air into another medium, making an angle of θ1 = 45.0° with the normal as in the figure below.(a) Find the angle of refraction θ2 if the second medium is fluorite. ° (b) Find the angle of refraction θ2 if the second medium is water. ° (c) Find the angle of refraction θ2 if the second medium is benzene.