Consider a region of space divided by a plane. The potential energy of a particle in region 1 is U₁ and in region 2 it is U₂. If a particle of mass m and with speed v₁ in re- gion 1 passes from region 1 to region 2 such that its path in region 1 makes an angle, with the normal to the plane of separation and an angle 0₂2 with the normal when in region 2, show that sin 0₁ U₁ - U₂1/2 T₁ = (¹ + 1 where T₁ = mv. What is the optical analog of this problem? sin 02
Consider a region of space divided by a plane. The potential energy of a particle in region 1 is U₁ and in region 2 it is U₂. If a particle of mass m and with speed v₁ in re- gion 1 passes from region 1 to region 2 such that its path in region 1 makes an angle, with the normal to the plane of separation and an angle 0₂2 with the normal when in region 2, show that sin 0₁ U₁ - U₂1/2 T₁ = (¹ + 1 where T₁ = mv. What is the optical analog of this problem? sin 02
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Theoretical Mechanics
Topic: Lagrangian and Hamiltonian Dynamics
>Generate the necessary equations to this system.
> Use the equations of motion
>Generate equations for (x,y), (Vx,Vy), V², T
> L = T-U
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For study purposes. Thank you!
Transcribed Image Text:7-8. Consider a region of space divided by a plane. The potential energy of a particle in
region 1 is U₁ and in region 2 it is U₂. If a particle of mass m and with speed v₁ in re-
gion 1 passes from region 1 to region 2 such that its path in region 1 makes an
angle, with the normal to the plane of separation and an angle 02 with the normal
when in region 2, show that
sin 0₁
where T₁ =
sin 0₂
- (₁
=
U₁ U₂1/2
T₁
1 + :
= mv. What is the optical analog of this problem?
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