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A fast charged particle passes perpendicularly through a this glass sheet of refractive index 1.5. Inside the glass, the particle emits light. The minimum speed of the particle is
- a)c/3
- b)2c/3
- c)4c/9
- d)c/9
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
A fast charged particle passes perpendicularly through a this glass sh...
∴ regractive index n = c/v
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A fast charged particle passes perpendicularly through a this glass sh...
Explanation:
When a charged particle passes through a medium, it experiences a force due to the electric field of the medium. This force causes the particle to undergo acceleration.
Snell's Law:
When a charged particle passes from one medium (medium 1) to another medium (medium 2), the angle of incidence (θ1) and the angle of refraction (θ2) are related by Snell's law:
n1 * sin(θ1) = n2 * sin(θ2)
where n1 and n2 are the refractive indices of medium 1 and medium 2, respectively.
Minimum Speed:
To determine the minimum speed of the particle, we need to consider the case where the angle of refraction (θ2) is 90 degrees. This occurs when the particle is incident at the critical angle (θc), which is defined as the angle of incidence that leads to a refracted angle of 90 degrees.
To find the critical angle, we can set θ2 = 90 degrees in Snell's law:
n1 * sin(θ1) = n2 * sin(90)
Since sin(90) = 1, the equation simplifies to:
n1 * sin(θ1) = n2
Rearranging the equation, we get:
sin(θ1) = n2 / n1
Taking the inverse sine of both sides, we find:
θ1 = sin^(-1)(n2 / n1)
Substituting Values:
In this problem, the refractive index of the glass sheet is given as 1.5. Let's assume the refractive index of the medium surrounding the glass is 1 (such as air). Substituting these values into the equation, we get:
θ1 = sin^(-1)(1.5 / 1) = sin^(-1)(1.5)
The angle of incidence (θ1) is the angle at which the charged particle enters the glass. Since the angle of refraction is 90 degrees, the particle passes perpendicularly through the glass. This means that the angle of incidence (θ1) is equal to the critical angle (θc).
Minimum Speed Calculation:
The minimum speed of the particle can be calculated using the formula:
v_min = c / n1 * sin(θ1)
where c is the speed of light in vacuum.
Since the particle is passing perpendicularly through the glass, the angle of incidence (θ1) is 90 degrees. Substituting the values, we get:
v_min = c / 1 * sin(90) = c
Therefore, the minimum speed of the particle is equal to the speed of light, which is represented by option 'B' (2c/3).
When a charged particle passes through a medium, it experiences a force due to the electric field of the medium. This force causes the particle to undergo acceleration.
Snell's Law:
When a charged particle passes from one medium (medium 1) to another medium (medium 2), the angle of incidence (θ1) and the angle of refraction (θ2) are related by Snell's law:
n1 * sin(θ1) = n2 * sin(θ2)
where n1 and n2 are the refractive indices of medium 1 and medium 2, respectively.
Minimum Speed:
To determine the minimum speed of the particle, we need to consider the case where the angle of refraction (θ2) is 90 degrees. This occurs when the particle is incident at the critical angle (θc), which is defined as the angle of incidence that leads to a refracted angle of 90 degrees.
To find the critical angle, we can set θ2 = 90 degrees in Snell's law:
n1 * sin(θ1) = n2 * sin(90)
Since sin(90) = 1, the equation simplifies to:
n1 * sin(θ1) = n2
Rearranging the equation, we get:
sin(θ1) = n2 / n1
Taking the inverse sine of both sides, we find:
θ1 = sin^(-1)(n2 / n1)
Substituting Values:
In this problem, the refractive index of the glass sheet is given as 1.5. Let's assume the refractive index of the medium surrounding the glass is 1 (such as air). Substituting these values into the equation, we get:
θ1 = sin^(-1)(1.5 / 1) = sin^(-1)(1.5)
The angle of incidence (θ1) is the angle at which the charged particle enters the glass. Since the angle of refraction is 90 degrees, the particle passes perpendicularly through the glass. This means that the angle of incidence (θ1) is equal to the critical angle (θc).
Minimum Speed Calculation:
The minimum speed of the particle can be calculated using the formula:
v_min = c / n1 * sin(θ1)
where c is the speed of light in vacuum.
Since the particle is passing perpendicularly through the glass, the angle of incidence (θ1) is 90 degrees. Substituting the values, we get:
v_min = c / 1 * sin(90) = c
Therefore, the minimum speed of the particle is equal to the speed of light, which is represented by option 'B' (2c/3).
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A fast charged particle passes perpendicularly through a this glass sh...
∴ regractive index n = c/v
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