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A trihedral prism with refracting angle ...

A trihedral prism with refracting angle `60^(@)` provides the least deflection angle `37^(@)` in air. Find the least deflection angle of that prism in water.

Text Solution

Verified by Experts

The least defletion angle is given by the formula,
`del = 2 alpha - theta`, where `alpha` is the angle of incidence at first surface and `theta` is the prism angle.
Also from Snell's law, `n_(1) sin alpha = n_(2) sin(theta//2)`, as the angle of refraction at first surface is equal to half the angle of prism fro least deflection
so, `sin alpha = (n_(2))/(n_(1)) sin (theta//2) = (1.5)/(1.33) sin 30^(@) = .5.639`
or, `alpha = sin^(-1) (.5639) = 34.259^(@)`
Subsituating in the above (1), we get `del = 8.65^(@)`
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Knowledge Check

  • A trihedral prism with refracting angle 60^(@) deviates a light ray by 30^(@) . The refractive index of the material of prism

    A
    may be equal to `sqrt(2)`
    B
    can not be greater than `sqrt(2)`
    C
    can not be less than `sqrt(2)`
    D
    none of these

  • A monochromatic ray of light strikes one face of a prism at an angle of 60^(@) and the angle of refraction is 30^(@) . The refracting angle of the prism is 60^(@) . What is the angle of emergence ?

    A
    `30^(@)`
    B
    `45^(@)`
    C
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    D
    `60^(@)`

  • A ray of light is incident at an angle of 60^(@) on the face of a prism with an angle of 60^(@) . Then the refractive index of the material of the prism is (the prism is in minimum deviation position)

    A
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    B
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