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Refractive index of an equilateral prism is √2

  • a)
    Minimum deviation from this prism can be 30o

  • b)
    Minimum deviation from this prism can be 45o

  • c)
    At angle of incidence = 60o, deviation is minimum

  • d)
    At angle of incidence = 45o, deviation is minimum

Correct answer is option 'A,D'. Can you explain this answer?
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Refractive index of an equilateral prism is √2a)Minimum deviatio...
Refractive index of an equilateral prism is √2

An equilateral prism is a prism with three equal sides and three equal angles. The refractive index of a material is a measure of how much the speed of light is reduced when it passes through the material. In this case, the refractive index of the equilateral prism is given as √2.

Minimum deviation from this prism can be 30o

The minimum deviation of a prism occurs when the incident angle and the emergent angle are equal. In an equilateral prism, the incident angle and the emergent angle are equal when the angle of incidence is equal to the angle of emergence. In this case, the minimum deviation can be 30 degrees.

Minimum deviation from this prism can be 45o

The minimum deviation of a prism is also dependent on the refractive index of the material. The refractive index determines how much the light is bent as it passes through the prism. In this case, since the refractive index of the prism is √2, the minimum deviation can also be 45 degrees.

At angle of incidence = 45o, deviation is minimum

When the angle of incidence is equal to 45 degrees, the deviation is minimized. This is because at this angle, the incident ray and the emergent ray are parallel to each other. As a result, the deviation angle is minimized.

At angle of incidence = 60o, deviation is minimum

When the angle of incidence is equal to 60 degrees, the deviation is also minimized. This is because at this angle, the incident ray and the emergent ray are parallel to each other. As a result, the deviation angle is minimized.

Conclusion

From the given options, the correct answers are option 'A' and 'D'. The minimum deviation from the equilateral prism can be 30 degrees or 60 degrees when the angle of incidence is equal to 45 degrees or 60 degrees respectively. These values are determined by the refractive index of the prism, which is given as √2.
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Refractive index of an equilateral prism is √2a)Minimum deviatio...
From
We can see that δm = 30o for μ = √2 and A = 60o
Further, at minimum deviation
∴ sin i1 = μ sin r1
= (√2) sin 30o
= 1/√2
∴ i1 = 45o
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