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Angle of a prism is A and its one surface is slivered.Light rays falling at an angle of incidence 2 A on first surface returns back, through, the same path after suffering reflection at the second silvered surface.Refractive index of material is
  • a)
    2 sin A
  • b)
    2 cos A
  • c)
    (1/2) cos A
  • d)
    tan A
Correct answer is option 'B'. Can you explain this answer?
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Angle of a prism is A and its one surface is slivered.Light rays falli...
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Angle of a prism is A and its one surface is slivered.Light rays falli...
Explanation:

Given: Angle of prism = A, angle of incidence = 2A.

To find: Refractive index of material.

Let us assume that the angle of refraction is also 2A. Then, the light ray would have passed straight through the prism without any deviation. But, the question states that the light ray undergoes reflection at the second silvered surface and returns back through the same path. This means that the deviation caused by the prism is compensated by the reflection.

Using Snell's law, we can write:

sin A/ sin r = refractive index of material

Since the light ray passes straight through the prism, the angle of refraction r can be calculated as:

sin r = sin (180-3A) = sin 3A

Using the triple angle formula, we get:

sin 3A = 3 sin A - 4 sin^3 A

Substituting this in the above equation, we get:

sin A/ (3 sin A - 4 sin^3 A) = refractive index of material

Simplifying this expression, we get:

refractive index of material = 2 cos A

Therefore, the correct option is B.

Summary:

- Assume that the angle of refraction is also 2A.
- Use Snell's law to calculate the refractive index of the material.
- Substitute the value of angle of refraction using the triple angle formula.
- Simplify the expression to get the answer.
- The correct option is B, which is 2 cos A.
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Angle of a prism is A and its one surface is slivered.Light rays falli...
Very good bro
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Angle of a prism is A and its one surface is slivered.Light rays falling at an angle of incidence 2 A on first surface returns back, through, the same path after suffering reflection at the second silvered surface.Refractive index of material isa)2 sin A b)2 cos Ac)(1/2) cos Ad)tan ACorrect answer is option 'B'. Can you explain this answer?
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