Two adjoining plane mirrors are separated by an angle of 100°. Light is incident on the first mirror at an angle of 70°. The lig
ht reflects toward the second mirror and is then reflected from it. At what angle is the light reflected from the second mirror?
2 answers:
Answer:
The angle is the light reflected from the second mirror is 30°
Explanation:
Given that,
Angle between mirrors = 100°
Angle of incident = 70°
We know that,
The incident angle is equal to the reflected angle.
We need to calculate the angle BCA
According to figure,
In ,
Put the value into the formula
We need to calculate the angle is the light reflected from the second mirror
Using relation of incident and reflection
We know that, i = r
So, i=r=30°
Hence, The angle is the light reflected from the second mirror is 30°
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Answer:
x = 2.33 R from the center of mass of the smallest sphere.
Explanation:
Due to the symmetry of the spheres, the center of mass of any of them, is located just in the center of the sphere.
If we align the centers of the spheres with the x-axis, the center of mass of any of them will have only coordinates on the x-axis, so the center of mass of the system will have coordinates on the x-axis only also.
By definition, the x-coordinate of the center of mass of a set of discrete masses m₁, m₂, m₃, can be calculated as follows:
In this case, we need to get the coordinates of the center of mass of each sphere:
If we place the spheres in such a way that the center of the first sphere has the x-coordinate equal to its radius (so it is just touching the origin), we will have:
x₁ = 2*R
For the second sphere, the center will be located at a distance equal to the diameter of the first sphere plus its own radius, as follows:
x₂ = 4*R + R = 5*R
Finally, for the third sphere, the center will be located at a distance equal to the diameter of the first sphere, plus the diameter of the second sphere, plus its own radius, as follows:
x₃ = 4*R + 2*R + 3*R = 9*R
We can calculate the mass of each sphere (assuming that all are from the same material, with a constant density), as the product of the density and the volume:
m = ρ*V
For a sphere, the volume can be calculated as follows:
So, we can calculate the masses of the spheres, as follows:
m₁ = ρ*
m₂ = ρ*
m₃ = ρ*
The total mass can be calculated as follows:
M= ρ* * (8*r³ + r³ + 27*r³) =ρ*
* 36*r³
Replacing by the values, and simplifying common terms, we can calculate the x-coordinate of the center of mass of the system as follows:
As the x-coordinate of the center fof mass of the entire system is located at 7.33*R from the origin, and the center of mass of the smallest sphere is located at 5*R from the origin, the center of mass of the system is located at a distance d:
d = 7.33*R - 5*R = 2.33 R